The team and league can't win. Let them co-mingle, then there's the potential for drama surrounding the team because of the stories that get out about the players and cheerleaders screwing around. Or even if they don't screw around, it still looks like they are, which can be just as bad. The "F" in "NFL" already has been replaced with a few different words, disparaging the league and making it look bad. If that were to happen we'd have yet another "F" that would start being used. So you get half of America disliking all the sex drama and who just wants to watch football, and the other half disliking the fact that players are "taking advantage" of cheerleaders and the team is "allowing" it.
Punish players that exploit or take advantage of cheerleaders, and now you have to deal with punishing a valuable part of the team who you pay millions of dollars to (because it's hard to find good players), when you could have avoided it by forbidding the co-mingling in the first place.
The easiest option is just don't allow the co-mingling. Is it really that big of a deal for a person to have to leave a restaurant and eat somewhere else? It's part of the job. A job that thousands of other women would love to have thanks to the exposure and how good it looks on your resume.