If you forbid the possibility of creating a certain number of alternative accounts, then the attitude towards their easy creation would change dramatically.
I talked about this recently in another thread:
I think theymos is not in favor of it, but I think the alts should be controlled in some way. It is good to have a couple of alts as many of you have, or even create another to say controversial things that someone wants to say without being recognized, but this to be able to create infinite alts that go building trust despite being a recognized cheaters or also create alts everywhere to question the reputation of forum members I think it should be put some limit.
There's no point in making a rule that can't be enforced.
How do many poker casinos determine that a user has already been in their system? They use an anti-fraud system, and this is not only a block by IP address but also many other fingerprints that the user leaves on the sites. All this, of course, can be bypassed, but this adds complexity for unprepared people.
I don't know if you're referring to how it works where you live, but in regulated Europe you have to pass KYC before you can bet with money. Without KYC you can still bet with play money but to play with money you have to send ID card or passport and maybe some other documents. Apart from that, Pokerstars has a great anti-fraud department.
In principle I would be in favor of putting some limit on the creation of alts but I think LoyceV is right that it could not be enforced. It would make things a bit more difficult, yes, but not much.