Why would Spaletti leave the team? I'm sure he has a lot more to target in Napoli. He may have received offers from big teams, but Napoli is his home. I think the chances of him leaving Napoli are pretty low. He has very good technical assistants. I'm sure they will make a better team next year.
Conflict with his boss, De Santis and as an employee for De Santis, Spaletti has to leave Napoli. No choice for him to stay no matter how Napoli fans love him and all he did for Napoli.
I don't know what happened with the conflict but I guess De Santis wanted Napoli to win Champions League too. He went to nothing at the season start to want to win two big titles, Serie A and Champions League. Media wrote a lot about the style of Spaletti to let his players play very attacking and ambitious in all matches, even in unimportant matches. I believe it is where the conflict comes from, as De Santis possibly believed that if Spaletti reserves important players for Champions League, gives them more time to recover, they would have been more ready and won over AC Milan.
My guess and who knows, only two people in the conflict knew the fact.
Another big coach might leave Serie A, Jose Mourinho. He loves Roma but he want to have more budget to buy some more players to make the squad stronger and have better ability to avoid effects from injuries. If Roma won't satisfy his demand, he will leave Roma.