And there are already encrypted media streams but I don't know if that counts as E2E?
A lot of these 'native' apps are just web browsers anyways...
So running WASM wouldn't make any difference if you're relying on a server to deliver you that WASM on every request. A compromised (or subpoenaed) server could simply ship you a compromised WASM payload for a single request and you'd be extremely unlikely to ever find out. If Signal wanted to add a backdoor, otoh, they'd need to ship it as a signed update to all their users, with all the reputation risk that entails.
Whether a native app is simply a browser underneath doesn't matter, just how the code gets delivered to the user. Even a browser extension or chrome app could work, since they are run from a signed, static bundle rather than from a server.
Encrypted media streams seem like a DRM feature? I don't think they have any relevance to end-to-end encryption.
So if you want real data privacy, you need a native app, despite the drawbacks you point out.