I'd expect the U2F protocol to be built into secure elements on laptops before a Type-C Nano comes into existence.
USB-C ports are too precious to keep them filled all the time with an authentication device, and there doesn't seem to be enough room in the male side of the Type-C coupling to allow the necessary circuitry to exist in a slim form factor. Both these problems are solvable, but meanwhile secure elements are already shipped with many laptops.
(An assumption of this comment is that the Nano is kept semi-permanently in the laptop port. That's what the Nano is indeed designed for.)
I think Web Authentication will slowly make U2F obsolete, in a sense that U2F will become one of many authentication methods, others could also be implemented. Checking WebAuth specs one can see references to Android attestation, TPM attestation so generally secure hardware elements. Implementing a U2F solution would require emulating USB exchange I guess.
Of course U2F still has an advantage that you can take your token and authenticate on a different device but unfortunately newer Yubikeys do not support U2F over NFC and there are not so many other solutions.
USB-C ports are too precious to keep them filled all the time with an authentication device, and there doesn't seem to be enough room in the male side of the Type-C coupling to allow the necessary circuitry to exist in a slim form factor. Both these problems are solvable, but meanwhile secure elements are already shipped with many laptops.
(An assumption of this comment is that the Nano is kept semi-permanently in the laptop port. That's what the Nano is indeed designed for.)