One important difference: HTTP/2 requires* encryption. This makes getting up and running for local development and small deployments more difficult. * https://http2.github.io/faq/#does-http2-require-encryption "[...] currently no browser supports HTTP/2 unencrypted."
I'm guessing they're not carving out a niche for self-signed certs? I think that would have been a fair balance, of setting a "this is a self-signed cert" instead of the current "YoUr WeBsIte IS UNSECURED" (which isn't actually true). Accepting and indicating self signed would also be handy in Tor's onion sites, since the only companies that will issue certs require EV2 and all your info and a pile of money. And Onio…
If you special-case self signed certificates, at it looks any less threatening, you will eventually have that page presented to unsuspecting victims.