Rysz, I think the OS forces you to have another admin before you can remove the last admin account.
I agree with your main point, removing all traces of the last user(s) can be tough. It's best to login to the store, purchase a suitable OS, then erase & start fresh with a new install. Otherwise there may be apps from the old user (which can prevent you updating from the store) or other associations to iTunes, iCloud or other services etc.
You may be able to use Internet recovery mode to download the OS that shipped with the Mac it may be a few versions old depending on your model.
Computers that can be upgraded to use OS X Internet Recovery - Apple Support
About macOS Recovery - Apple Support
I'd contemplate making a bootable USB installer to make the erase & reinstall process smoother after downloading the OS installer…
Create a bootable installer for OS X - Apple Support
Or use the app from diskmakerx.com