I think in the end it honestly comes down to a rider's focus on qualitative over quantitative and how that feeds back into their mental loop. For me, and this is a more personal example:
I deal with large scale data analytics and statistics for a living. Depending on the problem I am dealing with I can simply look at a bunch of points on a scatter plot and almost immediately get an idea of trends or lack thereof. Maybe run a t test or do a few basic tests for correlation, look at within measure variance etc and it's fairly easy to get an idea of what's going on in the big picture. What happens from there is simply a refinement of what I know as an expert of that data. Once myself or any other skilled analyst knows their data inside and out they often do not need to rely on much more than intuition and any models or statistical measures reaffirm what they already know or have observed. You could extrapolate this to power data. It doesn't mean that further analysis won't create more precision, but that additional precision might not change any related decisions.
The riders who don't use a powermeter but train might simply enjoy or find a bit more piece of mind stopping at that level of detail. They might use times on segments and basic summary stats like ride length or weekly hours. They could use heart rate and/or HRV just to get an idea of how their body feels. These riders are also the type who have a lot more mental stress about racing I've noticed. In others they take a more holistic approach to things, but remain focused on the overall picture and sensations. They might not go out and do specific opener intervals the day before a race, but they might still go ride and do something more by how they feel on the day and how they want to feel on the day of the race.
Just for experiment's sake I trained like this one season and we also had a lot of guys on our team that were ex collegiate endurance athletes that are now pro so I kind of figured I would have to ride for them in any race anyways. Put the Garmin underneath my saddle to just collect data and had a friend upload it once a month. Most intervals were done on feel or HR. I was pretty surprised at the end of this period that I could get within 10w of a target on a longer interval and that by using known times on shorter climbs I would be perfectly in specific zones. I also never rode indoors during this time.
There are those that are the opposite and feel that the only validation comes in having power data so you know what you did. That makes sense to, obviously, or we wouldn't be in this thread. I know quite a few people that train with power but have little to no clue what their data reallllly means. They do what is prescribed and send it back to a coach. This was me for a full season and probably when I had my best power throughout the year. At that point though the numbers were sort of ambiguous and more of a pat on the back when I could complete workouts perfectly, but had no clue how the targets were derived or what they meant.
Most riders are going to make 95%+ of their gains in the first few years of dedicated training. Whatever that training may be. Unless something they're doing is way off or they have a glaring weakness that they aren't intuitive enough to diagnose or need to lose a good amount of weight, then what remains is usually in the margin. Most riders also have no clue of what easier riding is until they use something to quantify what they're doing. The first period of working with any device that quantifies training bridges most of this gap be it HR or power, although power is clearly more responsive and often precise. A person can make a lot of gains by doing a smart, well-reasoned program of any sort whether its 2x20s, 5x5s, or whatever and power definitely facilitates that.
But not every rider benefits this much from power. I know that I personally benefitted a lot more from group riding because our rides were pretty hard and on similar terrain to our races and I was able to ride with riders that were much stronger and gained a lot of mental components I couldn't get doing standard intervals. I would often force power targets when I should have used HR and listened to my body. Dan Martin has described something similar with his training, but other than not specifically using power all the time I recall him being very detail oriented and very regimented. So, the riders that might not 100% need power might fall into this camp.
And in some areas of the country local racing and group riding is more than enough. In the Mid-Atlantic you can do at least one group ride every single day- a flat out sprint ride at Hains Point, a gravel ride out in Haymarket, a hill ride in Arlington, the weekly Greenbelt crit series, Wednesday Worlds up near Ellicott City, and of course the 7/10AM rides on the weekend, which have been going for decades and always bring out a large, fast crew. It's not structured, but if a rider has some skills and listens to their body and it's responses, you can hit every single possible physiological pathway and build up the mental side a bit more. And perhaps enjoy it because it is highly social. For some people this is more than enough.
To my point about it changing racing:
My earlier point was that these early gains used to come from people just riding, racing, and group riding. Usually riders then got to a point where they stagnated or got a bit overcooked and made the decision to be a bit more regimented with things. Or they were chasing a category or result goal and wanted to buckle down. A few years ago a powermeter was a big expense and not that common, so it usually was the result of a conscious effort to improve oneself. In 2009-2010 I knew relatively few riders with a PM and I only had a Power Tap because I got it on closeout when I needed a new wheelset.
I would say from then until 2012 less than 1/3 of riders I knew in the Mid-Atlantic used them and even then I recall very few people that were cat 3 or 4 that had one. Many if not most of the successful 1's in the area didn't use one. In 2013 there was a huge jump in usage. That was the year that I also recall a lot more lower grade riders using them and almost every cat 4 I met also had a coach and Zipps. By that point Strava was also fairly mainstream. That was also the year that racing really changed dynamics. The courses and races there almost never, ever change, but the dynamic did. In 2011 and 2012 there were teams that raced using normal tactics. It could be negative if it was one big team and tons of little ones, but it rarely was all that bad. In 2013 it was almost always incredibly negative and there was a huge increase in the number of crashes. There was a massive crash at a race in which a rider I knew caused in the sprint. We were friends and I knew that he had done dozens of sprint workouts. Yet, in the actual race he had no *f##k* clue how to judge distance and blew up 50m before the finish, then deviated his line to try and pull off and swerved into a few others.
He had had a coach since day 1, but didn't know what 200m looked nor how to actually sprint in a race. This is what I was getting at before. You'd see these riders upgrade to cat 2 and then do something a bigger 1/2 crit that might have elite or pros in the field and they would maybe be pack fodder at best, but hadn't learned a lot of skills in terms of cornering, tailgunning, braking, and how to apply smooth power around a highly technical course. These guys were the top 10 upgrades as cat 3s, but couldn't finish a single difficulty p1/2 race. I would estimate 25% still race today based on a quick glance at road results. But, this was also probably do to the USAC upgrade rule changes from needing all points in a single season to having no expiration. And local officials not really enforcing proper point allocation per field size.
Moving to CA I thought that this wouldn't exist, but it is by far worse hence my comments prior in the thread. When I joined a team here in 2015 all but two riders had coaches. Racing was harder here because it was even more negative aside from the 4 or 5 phenoms that are now pros that would ride away in climby races. There was no bike racing in most cases- no dynamic. When I say negative I mean that if a rider were to attack the field, the entire front 10-15 riders would match the attack and counter it. Teammates would bring each other back or bridge over. No one knew how to set a tempo or let a break keep a leash and pull it back. There was definitely no such thing as a leadout. And racing is declining here faster than anywhere in the country according to Road Results registration and retention data. Of the riders I met here when I moved here in 2014, about 10 are still racing. Most people that were on my team in 2015 have quit racing and many had never known a life outside of racing and training and just quit altogether. Quite a few of these people, including myself, had completely forgotten about the qualitative side of racing and riding and couldn't come to terms with not having that extra few percent from training or not following a training routine.
So, it can go many ways depending on personality but having been in quite a few sports that can easily be quantified I see the most burnout when the most analytic precision can be applied.