I think the reflections from glass will be about 5% of the reflections from polished stainless steel. So, while in general I strongly endorse your point, I don't think it applies in this context.
Is there any risk of the laser going through the glass and damaging parts of the machine? Or things such as refraction?
As I understand, those machines have a sheet of materials they can work with. This is probably the safest way to go: just stick with the materials the laser is made to safely operate on.