More specifically, are there any asynchronous use cases of CRDT that are very useful?
Say you wanted to build a rich text editor, which can't diff-and-merge as easily as with plain text. Instead of using git for version control, you can use CRDTs very similarly by fetching the remote state, merging with local state, and then pushing.
In that sense, you could build local first software with interoperable hosting platforms (like Github for git) [1].
See [2] as an another example but for a budgeting app.
[1] https://josephg.com/blog/crdts-are-the-future/ [2] https://actualbudget.com/blog/porting-local-app-web