Anything can be implemented in a kernel. But unless it's natively supported in other kernels, networks, and systems, that just means that one kernel is easier to work with.

The big idea behind TCP/IP is that it's a stack which you can use anywhere and everywhere. Not just any network, but any host. To do that, you need it to be portable and ubiquitous. And there is no protocol above OSI layer 4 that is ubiquitous. By nature of being above UDP, QUIC is layer 5 or higher. And it's got more features than other protocols do, meaning it needs more functions.

So not only is it unlikely that it'll be supported like the layer 4 protocols, it's unlikely to be supported by the Berkeley/POSIX sockets API, the one portable network interface specification for every operating system. One solution to all this would be to make QUIC a layer 4 protocol and update the sockets API. But nobody wants to do this because it's hard.

So, we could just have everyone add a layer 5 protocol to their stack, implement it in kernels, NICs, routers, etc, update the sockets API, and wait a few years for adoption. But will that happen? Or will the industry just go "let userspace handle it" like with TLS?