But courts have jurisdiction over their consumer markets, if a court in the US says it's illegal to use non-licenced data for training models and any product doing so can't be used/sold in the US you have lost access to a massive consumer market.

Case in point: GDPR, you can vacuum as much private data as you wish from non-EU citizens, the moment you touch EU-citizen data you must abide by the GDPR or you don't have access to a market of 400+ million of some of the wealthiest countries in the world.

You don't need global jurisdiction when your economical power is large enough.