I would say it's not impossible, but extremely impracticable. And since the official rapsberry pi keyboard looks just like it and is cheaper to boot...

I'd be interested in this is well, for the simple reason that this would de-clutter my desk when I'm using a desktop PC already and I wouldn't need to switch back and forth between two different keyboards.

It's somewhat similar to some all-in-one PCs where I think they don't look too bad, if only they came with a video input port so that you can use it as a display for other devices, or simply as a monitor should the PC part become obsolete some day.

From what I can gather, this is however not a built-in feature of the Pi 400 and will probably require some tinkering (which might be an interesting project in and of itself).

I also understand that the Raspberry Pi Foundation's goal is to offer this product at a certain price point, and that even though many of the wishes for additional features you can read in the comments here and elsewhere are each not unreasonable by themselves, every part that is added comes at an additional cost, and that they usually decide against it if it's something that is only used by a small fraction of the user base.