I am guessing he appreciates the aesthetics. (I would.)
This is an interesting idea, although depending upon where the shelter is sited, accumulated leaf litter and debris may be more of a noticeable issue with polycarbonate roofing.
However, Cowlitz, you might also consider Ondura panels. They are corrugated conventional roofing panels that are semi-rigid, lightweight, and durable. They require minimal framing and decking underneath is optional, so the added substructure weight will also be minimal. I have these panels on a couple of outbuildings I built that are still going strong in PNW weather after a dozen years. They are easy enough for one person to lift on a ladder and nail into place by himself/herself, and you should only need 4 to 8 of them depending on your design. They sell Ondura panels at Lowe's, and they are pretty affordable compared to many other types of roofing. HTH…
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