Unless you expect that most people would be fine with an unbounded number of flying cars (presumably at least as noisy as existing ones) without speed limits in their neighborhood, there's going to have to be some sort of infrastructure. Just because they won't literally be roads doesn't mean that the same types of social dynamics won't apply.

Presumably they would need roads in the sense of arbitrary "surfaces" on top of one another, so that you could shift lanes vertically as well as horizontally. And then you would need at least a visual indicator of which lane you're in, maybe even force feedback similar to bott's dots.

We would need a lot of landing pads free of nearby hazards (trees, wires, antennas). Those pads generally can't just be added on to existing buildings: most high-rise buildings weren't designed to support the necessary weight, plus roofs are already full of other equipment.

Assuming appropriate sites can be found, there will also be a long permitting process to get construction approval. The latest eVTOL aircraft are quieter than conventional helicopters but still loud so anyone living and working nearby is going to complain. I'm sure they'll also raise environmental impact concerns in many areas because the noise will prevent the endangered yellow-footed salamander from laying eggs or whatever so working through the mandated mitigation process also takes years.

Airplanes don't need roads either, but airports do a lot more than just provide hangars to store them and runways for them to take off and land. There's all kinds of systems to help planes avoid collisions too.

You might think it'll be very easy for flying cars to avoid crashing because they can just fly above and below each other, but that's also more directions for them to crash into each other from, more directions the drivers might have to rely on potentially faulty sensors where their vision is blocked. There might have to be invisible "lanes", maybe even with something like traffic lights, rather than having cars just flying every which way without external coordination.

Flying vehicles are fundamentally a different beast. They need to be light and are therefore more fragile. Also my car engine quitting while driving is not necessarily a life threatening situation. When you're a thousand feet above the ground just about any failure can be life threatening.

So no I wouldn't think flying a beater around is a good idea. People generally get away with flying unsafe planes now because they fly over unpopulated areas. They only kill themselves. Start flying over populated areas and you can wipe out a kids soccer game.

No, there cannot (at least not legally). Aircraft are subject to strict maintenance and inspection requirements based on both calendar time and operating hours, and a certified mechanic must sign-off on the completed work. Out in rural areas there are a few private pilots who fly poorly maintained "beater" light airplanes and get away with it because authorities never show up at the local grass strip but this is never going to be tolerated in urban areas.