If you really want, you can use almost any cloud-based solution that allows you to sync folders, with some caveats.

I use Obsidian with my Google Drive; it took me about 5 minutes to set up, and it works like a charm now. However, you need to set it up on every device you plan on using for synchronization. Also, you cannot work on the same document on two devices simultaneously. Otherwise, it works as you'd expect.

It's definitely messier than the Obsidian cloud, but for my needs, syncing it via Google Drive is more than enough.

Unless I misunderstood “cloud service functionality”, an Obsidian vault can be placed almost anywhere on the file system. For instance, a remote/WebDAV drive or even the Dropbox/iCloud Drive/Google Drive directory.

Migrating is as easy as moving the vault directory from one location to another, and pointing Obsidian to it.

As always, on iOS, there are some caveats as it lacks a traditional file system. So, the Obsidian app cannot access the vault directory on, say your Dropbox. But there are workarounds for it, like hosting the vault on a remote Git repository - which is what I ended up doing. Of course, this is a non-issue on Android.

Obsidian has a help page that goes in detail about what I just said.

As for the Git repository workaround, I referred to this article to arrive at my current workflow.

As an aside, I would like to touch upon my experience with using the inbuilt sync on apps like Agenda and Joplin - both offering syncing using iCloud and Dropbox while the latter offering a whole lot more. It is a flaky experience at best, wherein a significant number of notes never really sync between the devices. This forces me to use my phone to view a particular note while my computer for another. This is where the plain text file foundation for apps like Obsidian and Logseq wins me over.

There's a custom extension to sync Obsidian with a Git repository if you're familiar with that. Let's you sync up your notes as long as you have an Internet connection and access to whatever source control you use.

I’d happily pay a one-time fee to be able to use my own cloud service like Google Drive, OneDrive, or iCloud.

You can do that without paying. Obsidian vaults are just plaintext files on your disk. Just make a vault in your GDrive/OneDrive/iCloud sync folder and it'll be synced.

There's likely a extra hoop or two to jump through if you want mobile access, but it's not too much extra effort.

I've been trying it out for the last week or so as well looking to replace OneNote and this is the only issue I'm having with it too. I have it in my Nextcloud and can view notes on my devices but not create/edit them (I believe this is due to a permission issue with Nextcloud but haven't been able to dig too far into it yet). Other than that issue I love it so far.

Syncthing-ing the vault works for me. P2p instead of cloud.