Nothing is stopping me from hosting one but being able to use the custom sync server on my Android phone is essential to me. Setting up a sync server easily includes being able to use it easily in a sense of being able to enter its URL somewhere in the settings of the browser.

While I did not find any evidence that custom sync servers are supported on Chrome for Android, I have got the impression that the requirement of specifying the sync server URL as a command line argument for Chromium is a deliberate choice in order to decrease the usability of that option. Using a desktop environment, you need to edit the links to your browser application in order to specify a custom sync server. I guess the discussion on https://bugs.chromium.org/p/chromium/issues/detail?id=181429 is what mainly caused my subjective sentiment.