I kind of like honesty in "reality based" movies. Max Baer was no killer (as depicted). Howard needed a "bad" guy to make the hero look more heroic. It was unnecessary and cheap, aside from the fact that it indicates a lack of skill on the writer's part.
It makes for an interesting discussion. I argue the movie did not demonize Baer.
The Baer in the film was a libertine. True (I assume). Two of his opponents had died in the ring, or shortly thereafter. True. Do you think the historical Baer didn't cash in on how that enhanced his intimidation factor? Maybe did some trash talking? (By the way Craig Bierko's scary performance as Baer, the depiction of his physical presence, was great character acting and direction in my opinion).
Another film could be made that portrayed Baer in a better light, but I argue this one didn't cartoonize or demonize him beyond reasonable artistic license.