Taxi rates are almost exclusively set by local regulation

Right, in a free market rides are incredibly cheap and have a 50% chance of getting more expensive at the end when the driver who hasn't had a background check robs you.

Yes, but by and large that local regulation isn't divorced from actual costs--except perhaps to some degree in the case of fleecing visitors going from the airport to downtown.

That's not really true. Uber/Lyft have almost always been marginally profitable. Meaning they charge more for a ride than they pay the driver to perform it. Their massive losses mostly come from ridiculous overhead plus marketing to grow the business.

On the other hand, the taxi market never really worked because there's no price fluctuation to mediate supply and demand.

On one side you have places like Dallas, Atlanta, Phoenix, and others where taxis basically didn't exist for locals. On the other you had places like NYC where demand often outstripped supply. You wouldn't be able to find a cab or they wouldn't take you where you wanted to go.

You can also see it in medallion prices. They were so profitable in places like NYC people were paying a million plus simply for the opportunity to operate a cab. An obviously broken market.

That "marketing" budget is not going to billboards, radio spots and banner ads, it's going to voucher codes and driver "performance bonuses". It's just subsidies by another name.

Again, just not true at all. Here is Lyft's financial statement:

https://investor.lyft.com/news-and-events/news/news-details/...

They have 875.5 million revenue against 440.3 million COGS and 126.3 million in Sales and Marketing. Even if every dollar of sales and marketing was a direct subsidy they're still taking in 308.9 million as gross profit. Or, in other words, they're taking 35% or so of fares.

Part of Uber's (not sure about Lyft) marketing budget goes into subsidizing rides.

For new customers/drivers yes. Not really for existing ones.