Of course, this would only be effective if a gambler used one account in one casino. If a gambler, after each limit, moves from one casino to another, such restrictions make no sense.
Well, if a gambler has a few accounts at the same casino, it is shortsighted because it's already multi-accounting. In this case, a gambler risks running into a permanent ban and loss of funds.
Casino A can't do anything about a player having accounts on Casinos B and C. That's not their concern. What they can and should be focusing on is their own platform. If the set limits prevent the player from further gambling activities on their site and the player goes elsewhere, everything that happens afterwards is the responsibility of the player.
On the subject of multiple accounts. Casinos have ways to recognize multi-account holders and abusers, but such checks are conducted during withdrawals or account verifications. Abusers may think they have gotten away with it because their activities weren't recognized early on, but it can blow up in their face any day.