If by “default theme” you mean “the default theme for GTK applications and GNOME Shell”, then it’s expected: the default themes in both cases is embedded into GTK and GNOME Shell, respectively, as without a default theme both applications and the shell would be utterly broken.
I guess the actual question is: what is it that you’re trying to achieve.
I wanted to know if I could force a change to the default theme, by deleting all but one other theme.
I did a hard restart on my laptop (via the power button), on Budgie desktop. Since then, GTK / icon themes cannot be changed. I can change the values with the commands below (and they do, in fact, change), but it does not bring about any actual (visible) change to the themes:
gsettings set org.gnome.desktop.interface gtk-theme "example-theme-name" gsettings set org.gnome.desktop.interface icon-theme "example-icon-theme-name"
I asked at Ubuntu Budgie discourse, and it was suggested that perhaps gsettings were corrupted. I deleted all gnome user settings and reinstalled dconf, with no effect. Completely purging budgie desktop and reinstalling changed nothing either.
I thought Gnome desktop was affected as well, but actually changing themes is working fine when logged into Gnome. I hope this question is ok here, as it is about gsettings/dconf.
It now seems that a reinstall would be the next step. I am still mystified why a hard reboot would cause this to break though. I know very little about hardware, but my guess is this is some damage due to the power spike.
Thanks for answering a very basic question about how Gnome works.
If you are using a desktop like Budgie, in all likeliness GTK never sees your settings change, because there might be no xsettings-manager running (in GNOME, that role is filled by gnome-settings-daemon).
Adding /usr/libexec/gsd-xsettings to startup applications on Budgie fixed the problem.
Looking at the startup applications, gnome xsettings is there as /usr/lib/gnome-settings-daemon/gsd-xsettings, but this file no longer exists.
Notwithstanding, without the daemon running, changing all other gnome settings than the icon/desktop was still working… do these settings not need it?