> Cities that can go vertical rather than horizontal has tons of benefits

While it's a popular image in near-future scifi that doesn't look too costly at details, flying taxis with any current VTOL technology don't plausibly enable this, AFAIK, because while they can fly over cities easily, close proximity to solid vertical surfaces substantially disrupts the stability and effectiveness of VTOL systems.

That's why helipads tend to be either on top of or a distance from buildings now; even with a smaller number of VTOL aircraft, pads aren't at those places because it's the most convenient place for them, but because it's the only safe place.

I think that has less to do with strange aerodynamics and more to do with the deadly whirling blades interacting poorly with the solid vertical surfaces if there happens to be, say, a gust of wind. A ducted-fan based system would be much safer, and could work in a constrained urban environment.

Since we're imagining things, how about a network of skybridges between the skyscrapers, perhaps combined with elevator-like automated people movers? To me, that sounds more viable than flying cars in a dense city.

You mean like downtown Minneapolis? https://www.minneapolis.org/map-transportation/minneapolis-s...