RFID does work with base stations - I believe some toll roads use them. It's however impossible to deploy these at the scale necessary to make these tags work - the range is so short you'd need them every few meters.

No. I looked into this pretty extensively a few years ago. Ideally you could use semi-passive RFID, which only broadcasts a signal when its identifying signal is detected. But these still need a power source, and batteries are not cheap, only get so small, and don't hold a charge forever, so I don't think you can get the cost per tag for comsumers in such a system much below $10.

At that point, I think making them $25 and having them broadcast every 30 seconds so that they can be found anywhere in the world if someone walks by them with an iPhone is an obviously better solution.

Of course there are wacky solutions, such as using autonomous drones as mobile base stations to find fully passive RFID tags as a home inventory solution. But that introduces a whole host of issues.