I haven’t been able to run iTunes on Linux.

Run Windows or macOS in a VM? Bare-metal Hackintosh? I agree that it’s somewhat restrictive (and it would be great if iTunes ran on Linux, not that it’s surprising that it doesn’t), but it’s not horribly difficult to run your own self-signed iOS apps. If you can’t handle Windows or macOS, then you’ll have to plug your iOS device in to your Linux machine to use Cydia Impactor.

3 apps per device only.

Isn’t it per Apple ID? Not limited to 3 per device.

So you're suggesting to create multiple fake apple accounts and use them to build apps for personal use? I think that Apple would find out and ban those accounts, because surely they made that restriction to restrict exactly this behaviour (abusing developer account to by-pass AppStore). Does someone use that approach?

Fake accounts makes it sound like some “thing”. Just using a couple of different accounts for most any public-ish big service is pretty par for the course.

Not sure what “does someone use that approach” mean. I can just say Apple for sure does not do any sort of banning of any kind if you use a handful of accounts with one device.

There’s probably people in the sideloading and jailbreak community who have a dozen accounts linked to one device. I’ve never thought of it as anything more than just doing some simple relatively innocent thing to get around the 3 limit. No problems to the at this point probably dozen accounts I have.