That's an expected feature that only makes sense if you're part of a community that expects to share all communication.
On the Ardour's project's main IRC channel, it makes absolutely zero sense for the vast majority of people in the channel to be able to drop off the channel for 2 days, and come back and read everything they missed. The social expectations and norms there don't make this a sensible or reasonable expectation.
Contrast with "modern chat systems" ... in most of their uses, this is an entirely reasonable expectation because you are a _member_ of the group, and simply being offline isn't a reason for you to miss messages.
In our case (Ardour), we have private IRC channels where this sort of expectation is more reasonable, and we run a Quassel server to provide "always-on" messaging for people who are "members" (i.e. people for whom it's sensible to expect that they never miss messages).
where would they be kept? it wouldn't be the browser-based client that wrote and managed the log, surely, but (as with quassel), some server (e.g. the thing the browser talks to). and sure, someone could write a quassel-based in-browser IRC client. I don't believe it has been done thus far. That fact in and of itself points in the direction that others have mentioned: public logs of IRC channels are not part of the culture of IRC.
A browser-based client could persist the log in localStorage for basic history. It wouldn't capture conversation when you're offline, and it wouldn't store years of history or anything, but (1) it would solve the problem where the user refreshes the page and loses all their channel history and (2) nobody who is using such a web IRC client has a bouncer anyway.
