The first bicycle brakes were exactly that way. A metal spoon pressed down on the tire at the fork crown. These were reasonably effective, but the spoons would heat up and wear very quickly.

The key to effective braking is to dissipate the heat that braking produces. Since rubber is a poor conductor, all the heat of braking will go to the metal part. Rims are a relatively large heat sink, and provide decent surface for heat transfer to the air. Reversing the arrangement, means that the small spoon cannot take up much heat and has little surface to transfer it to the air.

In all vehicular braking, the real issue isn't how to create friction but managing the heat produced. You see this on cars and trucks, where they direct air flow over discs, and in some cases use steel clad copper discs to conduce the hear away from the surface faster.