You seem to be refuting your own argument with the Uber / Lyft example. Are these not tech tools that undermined the rent seeking of NYC taxi medallions?
The tech tools referred to in the story are only doing the latter; they aren't adding more rentable space and so are far more limited in what they can do about pricing or shortages.
[1] e.g. redirected taxis from long lines at major pickup points to sporadic pickups at less common places
The only similarity with Uber is that it would have made it easier to get a ride, but the effect would still be opposite of Uber with respect to medallion prices.
If you lived in NYC, you wouldn't see Airbnb as a solution but rather a problem created. It allows transients into buildings and we don't want that. We value our safety and pay for it financially.
The real solution is to undo the laws that create the artificial "economic rents" that benefit landlords at the expense of renters. See Economist Glaeser's column I cited above.
You can't really skirt regulation in the same way when it comes to building housing. People are going to notice when you try to erect a 50 floor skyscraper in a historical district.
If you want to increase the number of residences on a given piece of land, you have to replace single family homes with high-rises, no way around it.