It certainly would be nice if conflicts were synced. Even with the upcoming interactive conflict resolution project, for a large conflicts it would still be easier to resolve them on a larger screen.
My guess is the reason that conflicts are not synced is because of the possibility of creating conflicts of conflicts. I think however if conflicts were made to be readonly, and the code explicitly ignores syncing updates for conflict notes if the user was somehow able to change a conflict due to a bug, then it would be feasible to sync the conflicts (because they will always be created with a unique id), assuming that any partial conflict resolution would not be synced.