1 The torsional rigidty is shot. Convertibles, designed from the factory, have significant stiffening vs their hardtop counterparts to help with stiffness. It'll twist and flex like crazy if pushed. If pushed often, the cycling could cause fame failure.
2 The wing is now useless with the top down due to the turbulent airflow. With the top up it's likely much less effective as I doubt any CFD was done to the top to allow similar flow characteristics.
3 It's ugly (personal opinion)