What would cause an account check with compliance?
Anything that a casino could regard as suspicious behavior. Although it might be worth noting that the term "suspicious behavior" is usually not defined by any online casinos for the purpose of keeping their reasons a bit "fluid". In the case for example that someone is moving money in ways that could be seen as money laundering or if someone is using a bot to try to cheat the system or the player logs on with different IP addresses everytime...
The casinos need to make sure they are not involved in any illegal things like allowing players from forbidden countries to play on their casino or having their casino used to launder money.
If it were up to me, I would prefer the casinos did compliance check when the account was created instead of later on the grounds of suspicion.