The wood will move slightly when it's cut, so that won't work.

I am quite sure this can be countered - the wood could be clamped and the router could be tracked and the picture adjusted.

Further, the amount of movement would not make your routes completely useless/wildly inaccurate.

What you just described is getting halfway to a CNC machine.

Another benefit of this system would be portability. You can set it up and use it almost anywhere, like at a job site.

Having a system with clamps, overhead tracking, etc. is going in the wrong direction. It's not like the stickers are some huge inconvenience or expensive consumable.

And I am quite sure it can not. Just walking near the table will move it more than the stated 0.009" accuracy.

And supposing you could counter it - your method is wildly more complicated than a sticker. Why not just use a sticker?