They cannot (or rather should not) get in legal trouble in the country A where the business is registered. However if they travel to the country B, where their service is illegal they can be detained and put on trial for violating the laws of B. That could happen if the citizens or companies of B used the service of the cryptoexchange that is registered in A.

In the past that happened with at least one online casino allowed US citizens to play in that casino. The casino owner traveled to South America by air, then the airplane landed in a US airport for refueling and the casino owner was arrested while the plane was refueling.

A similar incident happened recently with Pavel Durov, the CEO of Telegram. His company was registered in UAE and provided services that were legal in UAE, but when he landed in France, he was immediately arrested because his company was violating the EU laws.

Also keep in mind that the country A, where the exchange is registered could have extradition treaties with EU or USA, so they can demand your extradition. If A is small, insignificant country it will easily bend over and extradite you to EU or USA, even if you are a citizen of A.

So yeah, you can get in trouble if you run a non-KYC exchange. If you decide to start such an exchange you should be careful and do your due diligence.