Ah, but that wouldn't change the ratio.

The gear ratios on a chain (or any gear for that matter) aren't actually a function of the teeth but rather of the diameter of the gear. Because the teeth are on a fixed pitch changing the number of teeth and keeping the spacing equal has the effect of changing the diameter, but it's the diameter that matters from a mechanical advantage point of view.

If you take an existing gear and break off teeth, the diameter remains the same and therefore so does the gear ratio.

The diameter of the axle and the axle support bearing is the limiting factor on how small the rear cog can get. At current chain pitch, that corresponds to 11 teeth.

DG