Good point and a downer if you need to hack with multiple EventSources. In any case, I see there's ongoing standardisation work on WebTransport including a DatagramTransport on top of QUIC: "It can be used like WebSockets but with support for multiple streams, unidirectional streams, out-of-order delivery, and reliable as well as unreliable transport."
https://wicg.github.io/web-transport/#introduction