Interstate highways (and most other freeways) are already bicycle-prohibited.

Car registration fees and gas taxes don't even cover the costs of road infrastructure anyways.

In a built-up city, a given width of street is far more effective as a pair of bike lanes than as one car lane. If you want to mandate bikes use bike-only lanes where available and sufficient*, fine by me.

*wide enough to safely ride the given vehicle, protected by something more than paint.