Personally, given the choice (which Shimano doesn't anymore) I like having all combinations available to me all the time. While I don't particularly like @RussellS's scenario of dropping to the small ring when you're in the small cog and big ring there are numerous other scenarios where a "bad gear combination" might be preferred, albeit just for a very brief time. And in @RussellS's case, if that's what he likes then why limit him. I'm sure he doesn't ride cross chained on a regular basis or for any length of time. He is conscious of what he is doing and fully aware of the pitfalls, but for that brief scenario, it's a welcome option. However, there are people, probably not many if any on this site, that don't realize anything about the pitfalls of crosschaining and so Shimano, rather than require these people to attend a course called "Shifting for Idiots" has, in their wisdom, just designed a system where the "Shifting for Idiots" course is not required. Yay, for the idiots. But I like to decide for myself how I like to use the gears at my disposal.
Imagine for a second if the current state of gears/derailleurs etc. had, from the beginning, never allowed us to cross chain the small ring to the either of the two smallest cogs at the rear. It would be something we just always lived with. Now imagine if a new system came out and was marketed where they said... "Now you have access to those two previously unavailable cogs no matter which chainring you are on". Pretty sure everyone, would go "Awesome!! Now, (in the case of a 36/52 crankset) when I'm cruising along in 36/13 and want just a bit more gear for little while for whatever reason, instead of having to shift to the big ring and shift up to the 17 cog, all I have to do is click into the 12 and voila, I'm there. Brilliant!!" (36/12 is pretty much the same gear as 52/17). No one is saying that you should ride in that combo for extended periods, but for those scenarios when you just want a quick snap, it's there much quicker than having to change both the front ring and the rear by several cogs.
Then there is now Synchro Shift and Semi Synchroshift. Aaach... Again, shifting for dummies candidates step right up. Which version would you like?... because you can't have it all, at least not anymore. At what shift points would you like the front to automatically shift for you? Decide now, because if you want different shift points we'll have to hook you up to E-Tube and change things. Or maybe you'd just like the rear to shift automatically when you shift between front rings. Oh, but how many cogs would you like it to shift automatically when you change front rings... 1, 2, 3, or even 4? But you can only choose one of those multishifts, or none, but please decide now cuz we're not hooking you up to e-tube while out on the ride.
Big/Big is another useful combo, say when cresting a slight hill that wasn't steep enough to drop into the small ring for that last little bit. And while that combo is available in non-synchro mode, it is not available in Synchroshift by default... you have to again go into E-tube to allow that.
Now, comparing this to my Campy Mechanical (and this is not a campy/shimano discussion, simply a shifting discussion)...
Every combination and every scenario that is available in either Synchroshift, or Semi-Synchroshift, or Non-Synchroshift is always at my disposal, instantaneously. Simulataneous shifts front and rear as fast as I can think it... and the choice of how many rear cogs I want to move along with the front shift is totally up to me, right there and then... again, so fast, and so easy. It's about being familiar with your bike and how to shift it. And every combo is available to me without any rub, either on the front derailleur or on the inner side of the big chainring when crossed in small/small, although I admit small/small is a combo I never use, but the point is I could and it would work.
Just more food for thought... Is Synchroshift an innovation?...Yes. Is it an innovation that makes riding your bike more or less pleasant and/or efficient? The answer is not so clear. For me it is definitely No.