The biggest problem is introducing more moving parts. Calibration and maintenance issues ratchet up. Not out of the question but something that would take some work.
I used to run a laser projection system that had pole mounted projectors at the end of a couple of hundred feet of fiber. In a several years of operation none of the galvanometers failed but a couple of the shutters did. While the projectors worked well we did have to re-polish the glass fibers on the laser table every eight months as the 60 argon laser would eventually fry them - that’s after splitting the beam half a dozen times.
Another issue might be with material thicker than paper. Your cuts are all going to be at different angles. Think kerf is difficult to figure out? It would be even crazier with the cuts being a fraction of a degree different.
Still, even with the shortcomings I think it has a lot of potential.
The laser would likely destroy the DLP chip. Galvanometer scanners are common enough that there would be plenty of ready made solutions.