I use iTerm2 that pops up F12, it's surprisingly close to that drop console behavior.

I use Yakuake (KDE's equivalent) for my password manager at work.

I find most DE's painful without that ability. The main exceptions are i3/sway or cwm, where I just launvh a terminal and then kill it.

I think that must be it, I use i3, so popping open a shell is always an easy option.

Never use sudo again! make the drop down be always at your root shell.

sv_cheats 1

I hadn't set this back up after getting a new laptop, but it's great for any of the one-off things you might need to do like confirm that some webserver is down like someone on chat complained it was, or lookup an ip or dns entry.

So the real benefit IMO is that it then lets you keep your actual terminals more clean and focused, and not just interleave that kind of stuff with whatever you are doing.