This isn't all that different to how I use my gaming PC - it's off in another room, with a monitor that is plugged in but almost always off (I don't think Windows will boot without at least something plugged in?), Steam set to start on boot, and then I entirely use it via Steam Remote Play from my main PC.
I did that for while, but recently switched to Bazzite. It's a much smoother experience.
I need a somewhat powerful GPU for work, so I'm seriously considering buying one of the more powerful handhelds with removable controllers and just taking them off. The screen would be superfluous but it's probably the most powerful travel PC, at least for the price, that's available right now.
I don't even need the battery that much. But all the options I've seen for SFF PCs that would fit in a backpack look fragile and I wouldn't feel confident carrying them around often. Plus, they're either expensive (because it's a tiny market) or geared towards office work.
On the other hand, the Mac Mini exists and is exactly what I'd want in terms of hardware. Why don't us Linux/Windows folks have this option?