Cyfer (
see here) also proposes a (albeit similar) solution.
The reason why my headphones are quit is that foobars internal volume is at max but windows mixer isn't. Sorry if I wasn't clear in my first post.
If I'm using the two speakers windows mixer remains unchanged when switching output, and if the speaker's own amplifier wasn't adjusted, music would truly be too quiet, but since it isn't so I use windows mixer to control volume because amplifier's controller isn't at all reachable from my computer.
If the approach of adjusting preamp in order to solve my problem by keyboard shortcuts wouldn't work well instead a alternative is what cyfer suggests (if I understand him correctly) or a new keyboard shortcut (inactivated) to raise master volume solely, or what I suggested in my OP, everything I said besides one needs to replace "preamp" with "master volume".
More clearly, if foobars internal volume is at 0db and user wants to raise volume level even more, foobar adjusts master volume level of all applications, all using one key for convience.