Ubuntu 20.04 change sound output device issue

Try installing pavucontrol and change your output device there:

sudo apt install pavucontrol
pavucontrol 

Worked for me so far as a quick fix but I can't tell you about the reasons why it works. Now I'm also able to switch output devices via the default sound settings again.

Some people also experience problems when timidity is installed.

You might want to have a look at these questions:

20.04: internal speaker (Audio) is not working in Ubuntu 20.04 LTS after upgrading from Ubuntu 18.04 LTS

No sound - Ubuntu 20.04 lts

A better solution is delete pulse audio config files in current user.

rm -r ~/.config/pulse/

Then logout & login or just reboot. Now you can change your audio device in system settings instead of pavucontrol.