Yeah De Zerbi is another candidate who might be a good replacement. I said Xavi because of thinking that he isn't actually a bad manager. He has managed Barcelona for less than 3 years time so he isn't very experienced.
However Xavi looks like a manager who knows how to work with young talents. He is giving the chances they need for their development. Besides Barcelona actually got a La Liga and Super Cup titles in the previous season. This season wasn't good enough but there are always ups and downs for most teams.

Anyways, when it comes to the reason of Pochettino's sacking it is hard to tell. It was a meaningless decision of the chairman.
He has a good knowledge of the Premier League and as well other coaches, he also had a good first season with Brighton but wasn't able to win something but then he qualified them for the European Europa League Competition for the very first time. Xavi Hernandez doesn't have that experience, he will need a season to settle down and understand things well. He has a good knowledge of football and all that but bringing him to Chelsea is not something I feel will benefit both sides in thr long run.
They can also look at Antonio Conte who is vacant. He is a good tactician and will help these talented players.
Roberto De Zebri also knows how to work with youngins, same way he with Shakhtar Donetsk and Brighton. He already expressed his desires to work in the Premier League Competition again immediately he parted ways with Brighton.
Todd Boehly should be smoking crack and stuff.
Todd Boehly done another attempt to bring instability at the Chelsea, and he sacked Pochettino while he has done good job in his first season which bring them into better spot and team having good depth which is help for the next season now who is coming it's not important because things are going to be instable with this decision.
Now who is coming its also important because we are having a long list of available coaches which are looking for the job and few are expecting Xavi which could be good choice but still question is can he do things which are important for the Todd Boehly instead of having good result De Zebri could be also good as he is already having good experience of Premier League teams and done good job at the Brighton.