Or
is there something in the tor design which would make any attempt to build
anonymous p2p on top of it unfeasible?
Not so much the design, but more the nature of the beast: Since you are creating an overlay network, you will need to find a way to transport all the data that users want.
That means you will have to have enough bandwidth to transport all the various filetypes that are the current p2p hype, in the end, on top of the bandwidth, you will have to encrypt and decrypt every single file exchange going on out there.
This makes it very unlikely that any overlay network would ever be capable, be it technologically or economically, to become big in p2p transports.
If you keep it small, yeah sure. But that kinda defeats the p2p way of thinking.