I wonder if bad behaviour is more common in the NFL than other leagues
I'm guessing probably not, though someone like Hernandez is, fortunately, fairly rare. A single player doesn't have as much effect on a team's fortunes in MLB, but it can happen. Addison Russell of the Cubs was suspended for domestic violence allegations prior to the 2018 postseason, and since the team lost a close do-or-die game, it's possible his absence made the difference--though it's also the case it was easier to cut him, because he wasn't peforming that well any more. Contrast this with two years before, when the Cubs won the WS. A key player was reliever Aroldis Chapman, who was suspended during the regular season for domestic violence. He wasn't with the Cubs at the time, but the team later signed him, to the rage of many fans, who felt the Cubs sold out. He arguably made the difference between winning the WS and not.
The loss of one player can have massive repercussions in the NBA for example.
You'd certainly think so, but I can't recall an instance when legal problems sidelined a key player. The late Kobe Bryant had to deal with a rape charge that had him appearing in court during the NBA finals, but I don't think he missed any games, and he avoided jail in the end. Plenty of other players have had legal problems--Jason Kidd, e.g.--but none that I know of resulted in being cut from their team. I think KC's cutting Hill was unusual, in that a lot of teams, in the NFL and in other leagues, would not been willing to put ethics above winning. As always, teams find it easy to cut players who aren't doing well--Ray Rice is a good example--but find excuses for someone who can make a significant difference.
The most impactful NBA example I can think of didn't even involve breaking the law. Draymond Green was suspended for one game in the 2016 NBA finals for picking up a technical foul that put him over the limit. That one game turned the series around. Same thing happened with Amare Stoudemire a while back in a playoff series--the suspension probably made the difference in the series. I think those two examples show how unwilling an NBA team would be to suspend a key player if it wasn't forced to.
Meanwhile, the Players Union now agrees not to have any preseason games at all. There won't be any games between teams till the regular season begins Sept.10--if it does, of course. I've been thinking these guys are going to be poorly prepared and not in ideal shape, but maybe the preseason isn't really that important, except for players on the edge trying to make the team. Many of the starters only play in the last preseason game, and then only for a couple of series.