A fighters power may diminish, due to decreases in speed. But in true relative terms their power is the same for the most part. It is their opponents that become tougher, bigger guy that can take a harder punch than a smaller opponent.
I disagree that power doesn't diminish. I think it all depends. If you have a guy like Tito, who could've fought at a lower weight but didn't have the discipline to stay at that ideal weight, you will have a guy who isn't in his ideal weight. So him moving up in weight will affect his power. On the flip side, take a guy like Hopkins, who had incredible discipline and stayed at a weight he could've by passed if he wasn't so disciplined. I think he's more powerful P4P at LHW then he was at MW. I guess most guys fall in between those two cases where they do fight at their ideal weight.
There's reasons why guys move up. Disciplined fighters like Williams, Pacquiao and Haye who's bodies are "growing" have managed to move up in weight without any trade-offs, but there are other reasons for moving up in weight... other reason like chasing money, over-eating or aging out of a weight class will all result in an increases weight without the increased benefits.
Agreed. The reasons why they move up has a lot to do with how their power will translate at their new weight and you mentioned those reasons.