There are plenty of decent portable monitors out there. I ended up with an MSI one, but I think any laptop brand can make a monitor (I also had some no-name one which had a nicer resolution but ended up breaking pretty quickly).
Anyway, I eventually concluded that I was wasting time re-inventing the laptop. It was nice to be able to put the unnecessary extra stuff, like the monitor and battery away, when using it in desktop mode (saving desk space). And the ability to pick a proper keyboard is nice.
But buying part-by-part has some downsides. You pay extra because this is all niche stuff, it doesn’t slip as nicely into a backpack (otoh if I only needed to bring the NUC somewhere, it could fit in my cargo shorts or bike under-saddle bag which was neat). And random integration things—you need to bring all the right cables, the battery probably doesn’t talk to your OS so you have to check it manually.
I also did SSH and VNC from an iPad, it works fine, you’ll probably want a keyboard and end up with something like a laptop, but extra latency and your SSH/VNC client will waste some pixels. I also did SSH and VNC from my iPhone, got a little stand and everything. That combo actually got interested questions in a coffee shop, so nerdy niche computing mission accomplished, haha!
So, I hate to ask the boring question because it was a really fun project and I got years of use out of it, but: Why not a laptop?