Let's say you use your own-run web server on your own machine (home likely for an individual, at the office for a small business), and https and/or a vpn between the phone and the server. Potentially all the way to a remote desktop or SSH to command line app. Let's compare:
> Privacy
For phone-hosted: threats of phone image screening, repair tech access, checkpoint demands, security bugs. For server-hosted: mostly just security bugs and working around phone cache.
> reliability and predictability
For phone-hosted: you'll never have all your data, you are constantly dependant on apps tradeoffs or outright availability (even my train schedule app stopped supporting my phone OS, amazing), phone theft or broken or other loss. For server-hosted: All your data, apps you control, always able to write your own additional tool and deploy whenever you want, reliable backups, against rare no network access.
> wanting to avoid setting up accounts
For phone-hosted: Indeed more and more difficult to deploy your own apps (because accounts and hoops to jump). For server-hosted: what accounts? My server my accounts. You rarely need something like an additional remote server (which even then would be less constrained than a phone developer account - and probably cheaper.)
> space (you didn't mention this one)
Server-hosted is much cheaper space than on the phone (at the tradeoff of transfer speed).
> development hurdles (you didn't mention this one)
Gone! Free as the wind! Whatever tool, whatever "pratices", no gatekeepers, update when you want either standard software or your own - or postpone updates when the situation demands. Absurdly simpler development. All yours.
So anyway, my point is that the original attractiveness of hosting a private-data personal app on the phone has changed. (1) that has been made harder - and less private, while (2) access of your home server has become MUCH better.