Oh I have had great success with making leather stamps.
Thick acrylic (~1" stuff) is great for leather stamps. They don’t need to be metal. Drill and tap the back and stick a thick lag bolt into it for something to hit.
When I did them, I was using a CNC. In which case a wide range of materials is possible. If you’re using the laser, it would be best with acrylic of course. CNC offers better depth control.
Leather is sensitive to feature angles. For example, if you simply make text “ATX” extruded vertically, the 90 deg corner of the letter structure will tend to cut leather. Now the first thing that comes to mind is “draft angle”, where the sides of the extrusion are angled, so the cross section of a square feature is a trapezoid. However, that’s not QUITE it. The edge itself can still be sharp even if there’s like a 22 deg draft angle. If the edge of a square feature was rounded (or beveled) even a little bit, it won’t cut the leather even if there’s no draft angle and the cross section is a square with slightly rounded corners.