...In his "training Bible" Joe Friel said that he sees the greatest improvement in "power to the pedals" by weight training. It is hard to believe that he would be 100% wrong, even if it is not as important as he might think...
Unfortunately Friel is wrong quite a lot of the time. Proof that people can improve in spite
of their training not because of it.
And its not usually the cardiovascular system that is the weak link, there are a whole host of other things which limit aerobic performance - mitochondrial density, ability to process metabolites, thermal regulation, delivery of energy/oxygen etc etc
Because the reasons WHY weight training may or may not be of benefit are still too murky to understand unless you really are trying to eek out that last 0.5% improvement there are many other ways that are clearly
understood to improve aerobic performance. It is even argued by some that track sprinters don't need to go to the weight room. If this is true then comparing the forces per pedal stroke being used by a track sprinter (especially in the first ~5sec) vs a road time trial and there is quite a disparity ie: if a trackkie don't need then a roadie sure as hell don't.
For work I have to be able to move heavy things hence I spend a decent amount of time with weights. I wish they helped my FTP kick along but as to date it hasn't helped a bit. And they haven't helped my sprint either. (I will note that in a n=1 study of myself I was able to maintain
Vo2max power by doing short anaerobic runs [Tabata protocol] and high rep weights for about 4 weeks, however, note it did not improve
either, FTP went down and I was heavier.)
As mentioned, the reasons why it might be possible for weight training to improve aerobic performance have been greatly debated, everything from type IIa and/or IIx fibre conversion, hormone response, dis-inhibition of the golgi tendon organ, hyperplasia of type I fibres etc etc.
The fact that it is so debated, when compared to riding the bike a lot (one way or another), no one debates that this will improve your aerobic performance. So you can do one exercise which may, just a tiny bit, improve your performance, or you can do the one exercise which will see vast improvement. Of course there are many ways to "skin the FTP cat" but just about all will yield far greater improvements than weight ever can.