If your shoulders are healthy and you are up to overhead pressing...explain to me how benching would benefit you more except for in a benching competition or pec size. As far as general strength and performence I'd look at overhead pressing over bench anytime. For that matter, I'd look at pullups over benching as a better general assessment. Don't forget that with bench you are laying prone and your body is stable. You don't have to stabilize you entire body against the heavy weight like you do in pressing. Bench pressing is easier than overhead pressing. Leverage is a very big deal with guys that can becnch a lot..not just true functional strength. You want to see who really has the most functinal strength then overhead pressing is going to really show it not that any one exercise is "the test".
There are just many reasons to promote it....including a better bench press. There is only one strenght athlete for which bench would be more important that overhead pressing and that is the powerlifter. Before that it mainly became popular because of the size it gave and because it was "easy". Strength guys used to not touch it because of how 'easy' it was compared to the stuff they normally did. Doing an exercise lying down? What are you lazy?
. That's the kind of attitude I'm talking about.
How much weight is on the bar is only one aspect of the benefit of a lift. The idea that the "heavier" exercise is always better is a misguided and ultimately self-defeating way to train. How heavy you can go on something has as much to do with favorable mechanics and leverage as anything else. In other words, it has to do with how "easy" it is compared to something else that uses the same amount or more muscle. Intensity doesn't always mean the same thing with different movements. Intensiveness, however, can tell you a lot about where your deficits are.
People likewise think that lat pulldown is "better" than pullups because you get the 150 pound dude handling the huge stack. But then that dude can barely do 1 or 2 pullups and would be hard pressed to find some functional benefit from the pulldowns like he would get from the pullups.
I'm not trying to say benching sucks and nobody should do it of course. I'm just trying to take it down a few notches to a more realistic level because there is really no reason anyone should be toture by a decision about what press to prioritize. If you want to improve your overhead pressing then by all means prioritize it in whatever ways are realistic for you. Don't let bench be the decding factor. A better press will likely lead to a better bench anyway and you won't be losing much in the long run by sometimes putting bench second.
Look at how Rip lists out exercises and you will see that he puts Press first in the list before bench pressing every time.