Does it not ultimately have the same problem? i.e. when you open obsidian, there's no guarantee the files are up to date as Android may have killed the third party sync program. And on iOS, there's no way for the sync program and obsidian to share the same filesystem short of the obsidian devs explicitly integrating
Android does have Content Providers [0], basically apps can provide a "filesystem" which isn't locally stored on your phone and act like Network Shares. Caveat is that you need an internet connection.
Good question, because it is indeed the default behavior.
But you can always tweak settings to run the 3rd party sync app always in the baclground, and override the battery optimization setting for that particular app.