Netsplits, hilarious lack of security (nickserv identify uses plain text passwords sent over an unencrypted TCP connection), you can't retrieve channel history, no support for threads, images, basic markdown formatting... Shall I go on?
Some of these are already in place, eg. IRCCloud can render simple markdown, supports push notifications, can show inline images, supports display pictures, Slack-like threads, emojis, etc...
An example: https://twitter.com/IRCCloud/status/971416931373854721
Hopefully longer term we won't need to use IRCCloud/a bouncer to keep chat history. AFAIK an IRCv3 server should be able to offer that natively (to an IRCv3 client).
As for unencrypted TCP... a lot of IRC networks seem to offer TLS these days.
Not saying this is perfect -- far from it, but people are working on improving IRC!
>no support for threads
That one's just wrong. You can make a threaded client if you want one, although it's not totally clear why you would since the CPU load of IRC is going to be very low in any reasonable situation.
Edit: Oh I see, threads as in forum threads.... just open a new channel. Otherwise, the concept seems to map poorly to ephemeral real time discussion. This is the first I've ever heard of AIM,etc of having forum threads.
Opening a new channel wouldn't work for fairly obvious reasons (nobody would be in it, you'd effectively have to do it for every single message, etc.).
IrcCloud is an example of a client that tries to solve pretty much all the issues and you can even plug it into a desktop IRC client and get most of the functionality including history. It's not necessarily better than modern chat or anything, but I love having a modern chat experience while being able to discuss things with people and groups who virtually only use IRC.
If you aren't a fan of hosted services you can run your own BNC. Some IRC servers have built in BNC services that give you things like better security and channel history.
Let me reaffirm that I am not of the position that IRC is perfect or modern. But you are misrepresenting it a fair bit, even in 2006 I was connecting with TLS (sometimes self signed certs though.)
No channel history, no threads, and no images are features.
There's formatting: bold/italic/underline and colours.