Oh for sure, IRC has a similar problem (except there are no images hosted on IRC).
But if the analog for a "private" Discord server is a private IRC server then in one you're trusting all the employees and in the other you're trusting yourself (or whatever admin).
And there do exist IRC client plugins that allow for E2EE chat (but I've never met anyone who used them).
IRC certainly has plenty of problems and Discord is very convenient but I think assuming privacy is assured on Discord is a bad bet.
