Can a rigid foam ceiling be left exposed in detached garage? – GreenBuildingAdvisor

So in my 2 car detached garage thinking about an unconventional approach. Can I lay rigid foam on top of the rafters and leave exposed? Not talking about cut and cobble just laying it on top just like you would insulate a concrete floor. So if you look through rafters you would see the bottom of the board. Polyiso maybe, or that Dow thermax. Thinking about using a reflective color to help with lighting. On top thinking about maybe minimal storage or nothing at all. Seems like a waste of space not to keep it something but I can see it as a junk pile. Would the entire top of foam need to be covered with plywood how thick? Do I need a continuous layer or can I put down boards only for laying items or standing in certain areas. Just seems easier to lay the rigid boards and tape the seams. Make a hatch door with weather stripping. Drywall is relatively cheap but if I don’t need layers of drywall or plywood on both sides that would offset some of the cost of using the more expensive rigid foam. The walls below I would use standard approach fiberglass batt insulation and drywall.

If I need to cover both bottom and top with plywood or osb, what thickness do I need since it is basically a foam sandwich.