They don't come to pool...they make cameo appearances in exhibitions and promotional matches, with the Mosconi Cup being the only real competition the top players of snooker have ever entered, and that has changed with the standard of pool players in Europe becoming better and better than the snooker players at the game. Top snooker players will never do what Alex P has done, simply because the money isn't worth their while. Even the lesser snooker players earn more than the top pool players excluding a select group of the elite pool players.
What you tend to see is English pool players taking up the American version, such as Daz. If you think American pool is in a bad state in terms of payouts and player earning the English variant is even worse. Some ex snooker pros like Drago have taken to pool later in life, and played at a decent-ish level. Nothing that's going to worry the top 50 pool players but then again, he's past his prime.