Agreed on nostr wasm client. Would love to see it. Probably one of the existing rust libraries need to target wasm and build the special sauce for it.
As a relay itself, still an advocate for wasm but not in the browser itself. I'm not a nostr expert but the need to be always online for other people to post to is pretty burdensome. Maybe you could do it if there's in depth support for specifying your personal relays when people are specifically trying to communicate with just you. Further, there's listening support that's required so a server needs to be running somewhere regardless.
Again, not a nostr expert but I'm sure there would be significant protocol work required to get to that point. Just because people can run their own relays doesn't mean the system can support it if everyone did. I have my own opinions about nostr but it's more of a distributed system than a decentralized one.