Several problems come to mind.
How would you repair damage to the covering? Tears on the aerofoils are going to affect the boundary layer. It would also look untidy.
I'd imagine the vinyl coating would start coming adrift around access panels and skin repairs.
Moisure might find its way between the skin and covering, raising a corrosion issue.
Then you have the problem of making the covering adhere around raised rivet heads if you're thinking about smaller aircraft.
There is also the colour scheme to consider.
I can't really see it working.