Well you can have client certificate on hardware. Some hardware even has attestation built in [0] so you can be sure that the private key is non exportable. PIV based smartcards do not require external drivers on most modern OSes.
U2F is designed for only one algorithm and allows a lot of optimizations (e.g the private keys are not really stored on the device but rather generated from master seed and origin). That's why they are substantially cheaper than PIV devices.
[0]: https://developers.yubico.com/PIV/Introduction/PIV_attestati...
U2F is designed for only one algorithm and allows a lot of optimizations (e.g the private keys are not really stored on the device but rather generated from master seed and origin). That's why they are substantially cheaper than PIV devices.