Sure, you can reimplement multiplexing on the application level, but it just makes more sense to do it on the transport level, so that people don't have to do it in JavaScript.
But you have to include giant libraries and kernel can’t see the traffic to better manage timing etc.
It only takes a few thousand lines (easily less than 10k even with zero dependencies and no standard library) to implement QUIC.
Kernel management of transport protocols has zero actual benefit for latency or throughput given proper network stack design. Neither does hardware offload except for crypto offload. Claimed differences are just due to poor network stack design and poor protocol implementation.
Not fully standards compliant since I skipped some irrelevant details like bidirectional streams when I can just make a pair of unidirectional streams, but handles all of the core connection setup and transport logic. It is not actually that complicated. And just to get ahead of it, performance is perfectly comparable.