Not that I think that you're wrong for wanting a more modern experience, it's clearly one of the main reasons IRC is losing traction. Some things can be solved client-side by, for instance, auto-fetching some URLs to display image links inline (although it could cause privacy concerns) but you also have limitations caused by the IRC protocol itself.
For instance IRC has no notion of "replies", if you want to quote somebody you generally copy/paste their comment and put your reply at the end. That's clearly primitive and makes it hard to find the original context.
Maybe. I am positive I miss 99% of replies (in "threads") in Slack. I always felt like the feature is designed for the case where you've already decided something, but people want to show up and bikeshed it, so they get a little area that nobody can see where they do that. Maybe that's not what it's meant for. But when I want to reply to someone, I say "@whoever, regarding foo that you were talking about earlier..." I think this is the IRC way of handling that and it seems correct to me. The reality is, sometimes you've missed your window to contribute to a conversation. No tool is going to change that.
The setup is not non-tech-person approachable, but its generally been untouched aside from updates in this setup since 2013.
For non-tech people https://www.irccloud.com/ seems one of the best on offer.
There's also an Android client, making it a pretty unified system. You can seamlessly switch between laptop and phone.