Using blockchain technology elsewhere sounds good to me since it works so well. Paying fees is the same as paying taxi fair. But who will the fees go to ? The owner of the cars ? A company ? These are things you need to think of first. But great idea.
Nice job thinking outside the box.
I guess that the fees will go to the specific cryptocurrency's network itself. Let's say that you pay for an autonomous taxi in a token that lives on the Ethereum blockchain. The fees will be in ether in this case, thus going to the Ethereum network itself (if the smart contract would be developed that way). But in any case, the smart contract developer can choose where the collected fees will go, so there could exist a possibility that a company would benefit from this.
If this idea becomes a reality in the mainstream world, it would totally change our society for the better.
EDIT: title should be corrected, the cars would not be blockchain powered. There's no energy in a blockchain. It's about managing their driving sessions in a blockchain, which is quite different.
I just referred to as "powered" in the sense that cars would use the technology itself, rather than being able to power the car with it. But I believe, that blockchains themselves could become a better solution to serve as a database, rather than relying on centralized servers like MySQL does. The advantages that the blockchain brings like no single point of failure, security, and more.
I'm hoping that blockchain tech would become so revolutionary, that would replace many of our traditional systems like databases, identity management, banking, healthcare, and so on. It would be up to the people if they adopt this technology or not. Just sharing my thoughts.