One possibility would be to use after-the-game replays only to punish particularly egregious behavior, like blatant dives, with suspensions. Wouldn't interrupt the flow of the game, but would deter wrongdoing.
dives are stupid and I hate them, but I think they are far overrated in the US (assumption from what I see in internet discussions)
Different sports, different "tactics".
The problem is ensuring the game is recorded fairly - they could use the existing cameras certainly but I suspect it's a non-trivial discussion to ensure that the camera coverage is fair for review purposes.