As DSL and broadband became more popular, chat moved to being more asynchronous. Chat clients started synchronizing message history with the server to make it avaialble on all your devices. It was easier to leave your presence online, even when you were unreachable.
IRC itself still retains a lot of that realtime chat, mainly because of its transient nature. Yes - the channel might be populated with people that aren't actually there, but the conversation is much more real time. Unless you have a bouncer or web client, the chat history starts when you join the channel and ends when you leave. There's no threading (ok, maybe some of the web-based clients will do that), so even if you see a conversation from a few hours ago, you can't participate in it. At best you can start a new conversation referencing the old one. Not everyone in the channel will have that history.
I consider that lack of permanence a feature. When Google Talk came out, I loved the fact that all my chat history was saved and it was available everywhere. Now that all chat clients have that, I find myself preferring the more ephemeral/transient chats.