Regarding your first subquestion, why is this not done in association football: The governing bodies are very much concerned that the game is played at all levels according to the same rules. Local club football would obviously not be able to use any kind of video review, and therefore the way players and officials approach the game at different levels would be different. For example, referees might be more or less likely to give certain decisions if they could review them on video, and players might play certain kinds of tackles more or less if they knew that video review could exonerate them.
It is also a concern that this would create more interruptions, but I think that is secondary.
Then, could an individual league do this anyway? Well, a league can do whatever it wants, really, as long as they comply with certain basics, like sporting codes and anti-doping regulations. They don't have to follow the official rules 100%. Major League Soccer, for example, has experimented with numerous rule changes. Or a league could play the whole game indoor on a smaller field, which of course many in fact do.
But if FIFA or UEFA, say, feel strongly about this, and I think they do, they could sanction anyone who tries by saying, for example, only teams that play without video review can participate in the World Cup or the Champions League. That would probably convince everyone. There are many quite benign regulations like that, in fact. For example, you need to play on natural grass if you want to try to participate in the World Cup.