Not to sound like a broken record.. but we have the 5 coaches that have already ignored him after seeing him in action.
Now that he's apparently free real estate, there are about 2-3 coaches IN THE WORLD who are willing to take him in. Mind you, this is a top 5 midfielder, a player who supposedly will become a better player than Xavi. 3 coaches.
At this point, I don't think he'll even have a better career than Alena.
I'll have to reply with a broken record then and say once again that Valverde wasn't really a question, Puig hadn't really presented himself yet and in any way, Valverde looked for a completely different style. Setien gave him full trust until he had already told the dressing room that he'll do whatever they want then, instead of doing his job. We know about Koemans treatment, very strange and unfair based on what could be seen in games.
What we really have is Koeman and now Xavi ignoring him. I did not predict Xavi to treat him this way, but in hindsight it is a bit predictable - Xavi is looking for players playing as predictably as he himself did, and he is also being as "safe" in his managing as he was as a player, taking the easy and obvious route instead of risking messing things up. The difference is Xavi had unmatched vision and technique, so his predictability on the pitch was no problem, and him playing it safe wasn't a problem either because his team mates also could give it back to him safely and progress the ball slowly and steadily until the moment presented itself. With Xavis Barcelona we see predictable, unforcing, safe midfield play leading to isolated poor wingers getting the ball to lose it via a failed dribble or cross.
Puig is a player who is not really trying to force things too much, but who is always looking for progress first and only then looks for the safe option - he is very creative and ambitious on the pitch. I think it hurts Xavis eyes seeing him get the ball and try to find options on the fly rather than just sleepingly circulate on the outside or backwards immediately, unfortunately. He wants his players to be patient and wait for the moment to present itself, but it very rarely does, his tactics are rarely really working, because the players are isolated and playing with too little or too much freedom.
Your canard about a free Puig only being of interest for three clubs is too stupid to respond to, really silly of you to take that as granted, and your attempted sarcasm there is just as silly, no one is supposing he'll become better than Xavi.