One of the simplest issues I can see is the search functionality, something I use daily in Slack and would sorely miss not having. Elasticsearch requires access to the contents of a message to index it (basic requirement).
Another thing that would become difficult would be adding people to a group, although my technical knowledge in this area is perhaps not massive, my thoughts are that if a user can join a group with another key, surely a Slack attacker would also be able to add their own key?
I'm sure there are many other things that ensure Slack cannot be E2E encrypted since it stops a significant amount of the logic they can do (they would become a dumb proxy), similar to why Google hasn't gone E2E.