IRC is lacking a ton of features. It doesn't even have a standardized charset! Nowadays people want E2E encryption, using multiple devices, multimedia, real-time audio + video, contact management, push notifications etc.
I use IRC. I use it with multiple devices, including desktop and phone. I have "contact management" and notifications (whatever push is) on both desktop and my phone. I use OTR for private messages. The only thing it may be missing is audio/video, but I think even that may be doable, I have not researched it due to lack of need.
I do not think so. I SSH into my Linux server where I run irssi (IRC client) inside screen (screen manager). Some people use IRCCloud. That is how I can use it on both my phone and desktop. On phone I use JuiceSSH, but I have used ConnectBot before, too.
I have notifications because my status bar and window manager know how to handle urgency hints and "bellIsUrgent" is set to true.
OTR is natively supported by irssi. Weechat supports it via a plugin. I do not know about other clients.
As for contact management... I am not entirely sure what it entails. Some IRC servers (such as UnrealIRCd, for example) support "WATCH" which is a notify-type system. The server will send you a message when any nickname in your watch list logs on or off. You can read about it more here, along with alternatives: https://ircv3.net/specs/core/monitor-3.2. There are a couple of different ways to achieve the same thing.
