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Can you just imagine the body/cowl flex on a vehicle like that? There is a reason why auto manufacturers stopped making 4-door convertibles decades ago.
It wasn't as big of a deal when all those cars from the 20's/30's were body on frame construction and they really didn't give two craps about weight.
Its a lot harder to make a unibody car into a convertible. Go drive an 80's Lebaron, Mustang, or Trans Am convertible, chassis flex and rattles will drive you nuts. Heck in the Mustang and Camaro you could twist the entire chassis with about another 100hp over stock in them if you didn't structurally reinforce the car. Although carmakers now have the technology on doing unibody convertibles to where you don't even notice any rattles or chassis flex on newer cars.