So much so, so naturally so, that you brought it up so, makes me wonder about what strife witnessed.
Digit
Hrmm... How far back can I roll this? Can I get my money back for the windoze-tax on machines I bought in the winXP era? :D
So the situation [there] is:
-
free software's principles are preserved for users of free software based operating system,
-
but if you use a proprietary operating system, you have to report your age to the pedovores... ? ? ? !
How rusty must the nail under them get before they move away? User lock-in got them trapped tight?
How long before we cease feeding the dragon tyrant?
~~come to devuan~~
come to antix
they listen.
come to devuan
Some are.
Thanks for reminding me to take my vitamins.
For all the stuff that can make us sad, depressed, anhedonic, etc, no point making it worse by not taking vitamins. D3 especially for the sads. RDA sunlight equivalent dosing.
Why are plants purple?
So you're the one.

if only implementation were the problem.
Good question.
Hrmm. First janky thought... "
ddthe running system to the USB". LOL. Dear oh dear, do not do that, LOL.Actually, first thought, before reading the post, just from the title, was "install gentoo", ... and that still works, ... if it's gentoo you want.
I wonder if you could do it from a virtual system... with whatever passthrough(?) or whatever needed to let it install to USB. So [in virtualbox or qemu or whatever] boot from whatever distro's live/installer [~ even, ventoy(?)], and install to USB, much like you would if running the live/installer on bare metal, except you're in virtual, and have access to your current daily driver OS and all your comforts there.
I noticed recently some distros do not like being installed to USB (~ is that a recent thing? Maybe I'd not been installing distros to USB from as diverse a pool of distros as I thought, and it'd always been like this.)
I feel like I'm forgetting some other obvious avenue. There may be just distro-specific methods. Like gentoo's stage3 handbook install method's already sufficiently flexible way [(or exherbo or decibellinux (oh noes, decibellinux.org is still down) or other distro that does a similar manual install)]. [edit: oh!]
... Then, depending upon what you need/want it for, and need/want avoid a reboot for, other options may offer solutions not considered further back in the decision tree... distrobox, bedrocklinux, distro-agnostic package management, manual (compile&)installs, or perhaps even just using something like virtualbox gets you far enough? ... But no, none of that's what you asked for. What you asked for is better. :)
[edit: oh!: I did make a start on a distro-agnostic distro-installer script, a decade or two ago, before life interrupted. I must have thought it possible. It would have allowed you to accomplish this. ... Pity "life" happened, or I'd surely have that made already. Is doable.]