You're totally right that you need a bot to have open logs online, I'm just trying to point out that a huge number of open source projects (CPython, FreeBSD, Haiku, Quotebrowser, random NASA weather balloons, thousands of others) already use a common bot so it's not that hard of a problem. The bigger problem is political, in that most IRC network discourage logging, and many communities are outright hostile to it.
Notifico discards PRIVMSG's immediately and the rest of its logs after a couple of hours normally, but in its last decade of operating it's seen more than 2 billion messages to give you an idea of how much has to get indexed.
Also, writing your own bot for IRC is trivial, and has no TOS, complicated APIs, OAuth flows, or other barriers to entry. Can absolutely do the same for Discord but they've already been making changes to make it more difficult to log or export your data.