Discord has shitty logging and log-search capabilities.
Discord's logging is shitty because:
1 - The logs aren't yours, they're Discord's. If you get banned from the server, your server shuts down, or Discord bans you altogether your access to those logs is gone forever.
2 - Unlike the logs of some IRC channels, Discord's logs aren't available on the web anywhere, so they can't be indexed or searched outside of Discord.
3 - Paging through hours or days of Discord logs is so incredibly painful, because every few screenfuls or so Discord has to load the previous/next logs and that is super slow compared to paging through text logs offline. If you have a lot of logs to page through, this experience is absolutely atrocious.
4 - There's no easy way to export the logs to be processed with standard/powerful text manipulation tools, like text editors, sed, etc..
Discord's search is painful because:
1 - There's no regex search.
2 - No ability to search via web search engines, because the logs aren't available on any website (see above).
3 - No way to search through the logs of multiple servers at once.
I have IRC logs going back decades, from servers I haven't been on in decades, but they're all instantly searchable, and the text in them is easily manipulable.
My Discord logs are trapped in Discord and I'm forced to use Discord's pretty but otherwise horrible UI to search them.
No, the reason Discord is popular has nothing to do with logging, but everything to do with how easy it is to sign up, join, and get a server running. Inline images and not having to learn obscure IRC commands or figure out obtuse IRC clients are also huge plusses for your average user. Discord's client is also visually pleasing -- something that most IRC client developers still haven't figured out. Aesthetics matter to users, as Apple has proved.
But Discord is an information black hole where data goes to die.