I can't agree with the assertion that the methods defined in HTTP since 1.0 are bike-shedding. I'll agree that lots of the the HTTP methods defined in standards other than HTTP are unnecessary cruft (particularly in light of the REST model) -- WebDAV and friends particularly -- but I don't see why you'd want to eliminate any of the HTTP/1.1 verbs (or PATCH) in HTTP/2.0, except maybe replacing HEAD with a no-content media-type in the Accept header for a GET request, and maybe dropping CONNECT and TRACE (though I suspect that there may be cases where they are used and critical, I've just never seen it.)
CONNECT is used to get a raw socket connection through a HTTP proxy. There'd be no way to get SSL/TLS to work with a proxy without it (save using SOCKS instead of HTTP to talk to the proxy).