[PaulDavisThe1st]

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.

[jamesgeck0]

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.