To the first point, I think we're saying the same thing, just differently. Of course it makes you stronger. I've never denied strength benefits. But I digress. I will attempt to restrain myself from continuing on that line of thought.
As to the second, this is a serious question, not an attempt to be obtuse. How can you hit a ball with more force than another guy at the same bat speed? Wouldn't the additional force lead to greater bat speed? If I am misunderstanding physics, I'm willing to be corrected. But the force imparted on a moving ball comes completely from how fast the bat is moving on contact, no? Obviously the contact point affects the distance, etc., but we've already established that is not a strength attribute. You could argue a heavier bat, but hardly anyone uses a bat heaving than 35 oz., in part because they can't, or don't believe they can maintain the bat speed. So two different guys, using the same weight bat, hitting the ball in the same spot at the same bat speed could result in different levels of force behind it? Again, not trying to be obtuse, serious physics question. I tried googling, but the best I could find was higher bat speed = longest balls, and real light bats are no good.