It's not that he doesn't fit Xabi Alonso's coaching style, it's just that Alonso hasn't tried to give Rodrygo time. Everything should be tried before being immediately judged unsuitable for any reason. Alonso also needs to have backup forwards if he wants to compete fiercely with strong rivals in major competitions next season. However, if Rodrygo's only reason for not being a starting player at Real Madrid is that he can rotate, as other forwards can easily tire if they don't get rotation in certain matches.
If he doesn't have the opportunity to play consistently at Real Madrid in the first team, it's appropriate for Rodrygo to consider joining another club. A player needs to have a regular place in the team so they can continue to develop their skills. Rodrygo is still quite young and has a long career ahead of him at Real Madrid, but earning a starting spot is a choice every player makes. Xabi Alonso could rotate to give Rodrygo a chance to play, but will that be enough for him? I see many quality players at Real Madrid currently in the same position.
Mbappe and also Vinicius in the Real Madrid front line are not easy to shift from the main place so it is not easy for Rodrygo to get regular playing minutes and indeed Rodrygo should go to another top European team to be able to play regularly and make his career much better, in terms of quality Rodrygo is quite good but the price set by Real Madrid is quite high so it is difficult for other teams who are interested in recruiting him.