Well, not to really beat a dead horse but I've already kinda experienced the opposite side of the oly lifting/gymnastics.
As some of you may know I've been really just doing strength cycles with rings and a pullup bar (+ weight added for pullups and stuff) for the past like half a year and even some before my knee got busted.
In terms of WODs like 30 MUs for time, I can put up sub 3 performance fairly easily (sub 2:30 with slightly bent arms + no eccentric) and most of the other stuff bodyweight stuff comes easy as well. On the other hand, with a prolonged effort like Cindy I am pretty sure something like the pushups would be the limiting factor into the 20+ rounds area.. so obviously NOT that great in extremely prolonged situations. Well, I'll let you be the judge; here's one of the more 'metcon + work after' situations I did recently (last Thurs):
30 MUs for time (full extension w/ eccentrics & ~regulation straps): 2:57
dynos for 2ft full hang: 3x of right, left, right left, both hands
kipping clapping pullups: 1x30, 1x20
After the 30 MUs I was able to do dynos (with just upper body) and more power work in kipping clapping pullups (made sure I made pullup level with every clap).
Other than random stuff like this I rarely do metcons at all right now. I'd say that's fairly good efforts for pretty much no metcon. Work capacity in probably sub 10 min efforts for at least upper body work is in "elite" CF range.
Now, considering I like to help people with gymnastics goals, when I look at helping people out it ALWAYS boils down to goals. So clearly, if what you need is mostly strength or power for your profession/job/whatever then that is what you need to focus on. Specificity is definitely important even with something like mostly CF.
I'd say if your goals are along the lines of GPP related there ALWAYS must be at least some form of GPP in your routine (generally probably at least once a week). Depending on your ability level, doing pure GPP may be better to a point (if you capacity is poor, but your strength exceeds your work capacity). On the other hand, if your work capacity is good and your strength is poor, you would definitely be more benefited by doing strength work. I think we can all agree on that.
Now, the real question is muddled a bit in obscurity: what about someone who's work capacity is poor and strength level is poor as well as someone who's work capacity is high and strength level is high. There's a couple of ways to approach this and my comments on the CF forum about doing something like SS first for the poor/poor person are what I stand by as strength is harder to gain. However, as you guys know GPP and strength tend to return diminishing gains as you improve. At what point should there be a strength/power bias over GPP? Well, having not given this much thought I really don't know myself. All I do know though is that I can put up fairly strong short-medium effort workouts with my "high" max strength in gymnastics (really more like low-intermediate in REAL gymnastics terms) as can Donnie (to a MUCH greater extent) on Oly because of his enormous power and strength.
In JUST speculating this is probably what I would have to say on this topic. Namely, I would say a mixed power/strength and GPP hybrid would be a good idea. CF workouts themselves are SIMILAR in nature to the extent that you have your max efforts (recently C&J 1-1-1-1s, metcons (girls) and endurance (5k, 10k, etc.) type workouts. The main thing we have to look when comparing something along the lines of a power/strength + GPP vs. CF is generally that there's diminishing returns because you're working all aspects rather than specializing on say just power, strength or endurance. On the other hand, what I'm saying is virtually the same thing in respect although slightly different. If GPP is randomized via something like CF and volume toned down slightly (besides occasionally for longer efforts like heroes) in regards to either metcons/endurance, then you get a slightly more strength/power biased program which is theoretically more effective if strength/power give better returns to GPP. Given that we have a high frequency the high conditioning level is definitely a factor here that would prevent people with less work capacity to do such a thing. Basically, it would just boil down to something like maybe 1-3 oly lifts/gymnastics strength and then CF afterwards.
The one criticism I have with this is again the diminishing returns you get when combining power/strength work with endurance biased work that you would generally get with CF's metcons and endurance runs. However, this is basically the inherent dilemma that we're going to face regardless as there is always going to be a tradeoff. Biasing it a little more one way or another is going to give significant decreasing gains one way or the other. Adjustment therefore needs to be either slightly more power/strength or endurance biased FROM CF's GPP standpoint to achieve greater GPP. Again, I think this goes bak to goals.
The only thing I can see with certainty that will increase gains is higher frequency. With higher frequency it's pretty obvious that you get faster adaptations as per a 3/1 cycle you're gonna have about 3-9 lifts per week + 3 "CFs". However, obviously this may not be as sustainable in the long run and can lead to overtraining/overuse more easily... but that's not something we're going to worry about.
To be honest, I don't think there is really a clear cut answer to the question. Especially in modifying something like CF it may be arbitrary to shift a bit of focus towards strength/power biasing workouts a bit more... but are the gains worth it? I dunno.
Anyway, yeah, I guess that's it.
p.S. Wanted to add that max power is generated at about 40-50% of 1 RM IIRC. Although not sure if that would be the case if you were combining multiple exercises into something like a metcon. But I do think that by playing with the numbers depending on the exercises you can do you can "maximize" power if you want to call it that.
I know there's been pretty big discussions on power vs form so I'll leave it at that for now I guess.
P.S.S. Most *male* elite gymnasts are in their 20s and early 30s. There's just a few olympic level gymnasts and they're usually in their late teens. It's the girls that tend to peak earlier (before massive puberty growth spurts and such that decrease strength to bodyweight ratio and such). Guys just tend to keep on getting stronger which is great especially for events like rings. People like Jovtchev who were once the exception are now getting relatively more common at least with the men.