I don't think so, no, or rather, I think you might lose out on "the web" part of it. That is, that the web really is a bunch of stuff, all accessible in one "thing", and stuff can and does "link" to various other stuff.
E.g., consider an OIDC log in. It's really one app (the relying party), redirecting to a whole different app (your SSO of choice). You can't exactly do that in another app without, I think, really running into issues of "is it my SSO, or a phish?". The browser provides that trusted layer of "I am look at this app" (via the URL bar). And even then … that's fraught with absolutely immense tons of peril.
It's also a distribution mechanism: I don't have to download Slack, Discord, Postman, etc. — I just go to a URL, and the browser downloads the code needed. (I can and do download some of these, and there are some advantages to do so. But then extend it to every app I use on the web: my bank, Turbotax, my email, my three different loan payment sites, my landlord's payment site … that'd be far too many downloads.)
