My thoughts on 'strenght', as it applies to boxing, have a basis in "the proper amount applied in the proper way at the proper time." I think that there is too much emphasis put on being 'strong' physically, not enough on being strong mentally. After all, you don't need to press the rival over your head, just hit him while making him miss you.
I think that a great deal of that is conveyed mentally. Certainly, your body needs to be fit, to go the distance required at the pace required, but that starts in the mind. Because you'll never make the effort to be fit in body if your head isn't right. I've never believed in weights- bulk you up too much, to a weight class beyond your other attributes- and have always favored flexibility and leverage. Oddly, everybody I've worked with is considered strong inside and a very hard puncher. Properly applied force.
When I'm teaching somebody, I focus a lot on where you put your weight: I think we can all agree that an individual that can put his weight in one place and focus it is a very strong man indeed, whether or not he can bench press a ton. I try to focus their mind on their capabilities, and the fact that I expand those capabilities- not for ego reasons but because, at some point, they may very well need to believe in me when it is hard to belive in themselves. (This is especially true when working with young kids).
I don't like jumping rope as a warm up exercise because it is brain dead and repititious. Shadow boxing is much better because it engages the mind, and mental strength is the foundation. Then there is me, constantly over the shoulder, because you have to know what you are thinking, and what you are trying to accomplish, as you shadow box, hit the bags, and so on. When you build the mind, the body has to follow, because then you know what you are trying to do and can prepare accordingly.
Personally, I think strength is overrated. Take Saddler-Pep...Saddler was able to over power and manhandle Pep inside, thus he beat him. But only because he made Pep lose his mental strength and get ouit of his game; in the fight where Pep kept his cool, he won.. (Of course, this gets back to properly applied force and Pep couldn't/didn't punch much...)