Just to clarify that Estonian anti-money laundering chief does not have the power to revoke crypto licenses. Depending on how it is handled it might need a legislative changes to do something like that. As I stated in one of my own posts this chiefs word does carry a certain weight, but there are also others like him who have contradicting opinions. Quite a lot, in fact.
What will happen if the platforms refuse to cooperate? Of course, other parties will be contacted and asked to confiscate the platform, or at least stop it from working.
If the government is serious, more legislation will be imposed, but the goal appears to be to reduce Estonia's view as a safe haven for every crypto-related platform or exchange that does not want to comply or take advantage of low fees.
Does anyone know if a famous platform is based in Estonia? They will be tough with the users.
I am a bit out of my depth with this so take my answer with a grain of salt. Depending on how the un-cooperating company is set up a lot of things can happen or very little. If a company loses their license but still operates in Estonia it can be grounds for criminal proceedings in which it´s operations can be suddenly halted and its inventory confiscated. The efficency of the criminal proceedings depends entirely on how the company is set up. If operating in Estonia is merely a legal fiction (meaning that factually speaking the company operates somewhere else) a criminal proceeding in Estonia can have little impact on day-to-day business of the company. For example if the companies leadership, workers, main bank accounts, servers etc are outside of Estonia (and outside of EU), then there is very little that can be confiscated or halted.
Also a company who does not want to cooperate can litigate license revocation in the court for quite a while. This further minimizes the risk that a company can suddenly become illegal. If the government decides to revoke the license suddenly then a company willing to go to court can additionally claim that it is unlawful to impose such a drastic change without first giving a reasonable timeframe for interested parties to react to those changes.
I found a website here that lists platforms that are based in Estonia:
https://craft.co/cryptocurrency-companies-in-tallinn-ee?page=1. Not sure how many of them are famous, but I do recognize some