If a regulatory change harms consumers, what's the point of deregulating?
San Francisco might benefit from deregulation, because there are political problems and structural breakages in their system. But the Chicago and NYC cab systems work pretty well right now as far as I can tell.
Incidentally, while I agree that medallion caps are anticompetitive and an artifact of old price-fixing schemes, they have a beneficial effect of making it expensive to operate a licensed cab, which creates incentives for cab operators to avoid some negative externalities of their business (like running people down, or operating blatantly unsafe vehicles, etc).
Taxi revenues are currently $91k/year in NYC. Breakdown: $18k medallion, $50k labor, the rest is maintenance/insurance. If labor costs were reduced to $35k/year due to competition (taxi driving isn't exactly high skill labor) and medallion costs were cut in half, that's a 25% reduction in taxi cost.
http://www.nyc.gov/html/tlc/downloads/pdf/presentation.pdf
I think my proposed $9k/year would be sufficient to pay for taxi inspections to get rid of blatantly unsafe vehicles. As for running people down, current incentives not to do that seem sufficient. It's no more a problem to be run down by a taxi than by a Dominos driver, who has the same incentives as a taxi driver. In fact, Michael Q. Lateforwork has even less incentive than any taxi driver to not run people down - he won't lose his job for doing so.
Similarly, most people who deliver pizza are not career pizza delivery drivers. A pretty big chunk of them are students. Their incentive not to wreak havoc isn't the loss of their pizza job, it's in not screwing up their lives and bankrupting themselves.
That said, you have a good point. And I'm not HN's official advocate for taxi medallions. I just want to point out that while it certainly wasn't the intention of the medallion system, or even its primary effect, artificially-limited medallions do create a scarcity value to them that incentivizes drivers to play nice with the rest of the system.
There are plenty of unlicensed cars out there, and there is a clear difference in how reliable they are.
I wouldn't vote against any sensible replacement scheme, and yours sounds sensible.
May that you never be in charge of taxi service.