With tasker, DAVdroid would not need any more privileges and code (except the plugin interface)!
Tasker is an automatisation tool that is quite flexible - and you can chose from many triggers (like on connect to a certain network / time intervals / …) and actions. Many actions are provided by tasker, but other 3rd-party-apps can provide these actions as well.
My point is that with a tasker plugin, all my use case examples can be handled by the user itself. However, I have to admit that tasker is quite a complex tool that is not fool-proof - so it not widely spread, and just used by some “geeks” - but it has 1000k installs, and people who want to use DAVdroid are not beginners as well
Sorry that I can only contribute the idea. I have experience in coding for real time embedded systems, but no android experience…