In my opinion someone who wants to get a sponsorship in any sort of sport has to be dedicated, focused and behave like a genuine athlete. There might be some exceptions in the American pool scene, but it's totally different in Europe. Look at all the European top players. They are athletes, but not necessarily fitness-wise. They are highly professional in practice and in tournaments ON and OFF the table. This professionalism is exactly what it takes to get sponsorships in Europe (besides some other minor factors).
You have to be profitable for a sponsor and represent their brand as good as you can. The best examples I have in mind are the Ouschans. Albin and Jasmin are sponsored by their home county and other local businesses from Klagenfurt. They don't take it for granted though. They regularly mention their sponsors on their social media platforms, do collaborations with them and so on.
As an actual athlete you have to work with your sponsors, it's a give and take and it certainly is a lot of work besides just playing pool. Maybe a lot of other players don't want to put in that extra work or don't want to take that kind of responsibility. Just look at the online presence of the top European players in comparison to American players. European players advertise themselves, they keep their followers updated and they are grateful for what they do. For me THAT's the difference in American and European pool these days.