Most things in slack are available in some form with irc, but not preconfigured out of the box. And some things on irc can take some fiddling to get set up right, and you can't count on everyone else to have enabled support.
But I would love to learn how to do that, for example with ZNC which is online all the time.
That logs the logs in an SQL database, you can search with Quassel-Suche (a web-based search engine for quassel backends), and we have clients for Windows, Mac, Linux, iOS (kinda) and Android (with a better Android client in beta) and a webclient.
You get contiguous logs like in Slack, Push Notifications (with the Android beta, soon), and you can search through your logs.
In fact, I don’t bookmark things in my browser anymore – I send them in a query to myself, and just use quassel-suche half a year later to find them, or, if there hasn’t been much activity in the channel, just scroll up (infinite scroll to load more logs).
Most open source projects can not pay for the archiving feature - so messages are deleted and gone forever.
They aren't deleted and gone forever. They're simply not searchable. If at some future point you decide to pay, your entire history is made available to you.
I realize that doesn't help projects who will never want or be able to pay, but it's an important point for those who might.
How you search the created logfiles is up to you, znc is not a log management system, it merely creates.
There's also services like https://botbot.me that offer easy setup of this
