When I used to do a lot of singles on bench presses, I was able to knock off 225 20 times for reps at a bodyweight of 188lbs. I never trained the bench press for endurance and did not really need to. Part of it had to do with the fact that after training with 350+ for singles, 225 felt like nothing. Same with the dips and chin-ups.
Now, I doubt that someone who train the bench press for sets of 20-25 will improve their one rep max and I will tell you why. For one, you never get used to handling heavy weights. If you train with 225 all the time and then try to lift 350, it is going to feel like a ton, but not the other way around. Your central nervous system never comes into play and also you do not have to respect the weight when doing high reps. You really only have to concentrate on the last few reps(Unless, you are doing the Super Squats 20 rep program in which every rep is hell).
Let me give you an analogy, If I am a professional fighter, beating up inferior fighters will not prepare me for superior fighters. However, beating superior fighters will make the mediocre ones feel like nothing.
An example of test driving this idea is to do weighted pushups. If your goal is to do a lot of pushups, try doing pushups with a 50lb sandbag on your back. Once you can do 10-15 easily, try doing bodyweight pushups and watch your numbers fly up.
Will this work for everyone, I have no idea. Regardless, it definitely works for me. Give it a shot and let me know what you think.