What if extension headers made it better? We could come up with a protocol consisting solely of a larger Next Header field and chain this pseudo header with the actual payload whenever the protocol number is > 255. The same idea could also be used in IPv4.

I didn't mean to imply otherwise. But, as you say, this is equally applicable to IPv4 and IPv6. There were a lot of issues solved by IPv6, but "have even more room for non-TCP/UDP transports" wasn't one of them (and didn't need to be, tbqh).