Umm libera itself allows "easy anonymous registration". You don't even need to have an account. You just join with a made-up name if you want to.
This is in fact one of the things I love about IRC. Nothing wrong with it but it feels wrong calling matrix out on that.
The archiving makes kinda sense for matrix' features of scrollback on demand. I believe there's an IRCv3 feature for it too. The bridge should have a provision to prevent users to see any backlog from before the moment they joined.
Ps I really hate those new "single puppet" third party bridges they recommend. Because they break nick colouring and also the actual nick of the user speaking is in a different place. Having each matrix user have their own IRC puppet is much nicer on the IRC side. Especially when there's more matrix than irc users.