Yeah, we definitely utilized our laser cutter in a similar way. To test form and fitment, or small scale development, we prototyped with acrylic sheet. It cuts very easily, no nasty fumes, and it is relatively cheap (we had a ton laying around from an old sponsor). To bring up the talons for our arm, we cut panels and 3d printed pieces to make a functional model- not resembling the actual arm in any way. It’s great for that. The models you are quoting likely have more power than ours, but our experience with thick plywood has not been great, unless you really love a campfire smell in the shop. Our router still cut it faster, but we weren’t utilizing it nearly as much as it sounds like you guys are, thus we never hit that bandwidth cap.
So given that you already have a router, a laser cutter is definitely a good buy, but there are still machines I would buy first if you don’t already have access. Printers capable of printing Nylon or Polycarbonate reliably would top my list, followed by a CNC Mill (having access to a Haas has been incredible). Not to mention the manual mills and lathes that made the majority of our components.