That's not an intrinsic problem with IRC-the-protocol. The only technical issue with it is the lack of server-side channel history scrollback which makes it inconvenient for users who aren't connected 100% of the time. This could have been entirely solved with a single extra server command - "/fetch-channel-history". But I suppose no one was convinced of the need.

If you wanted to make a modern, user-friendly chat application that relies on central servers, there's no reason not to base it on IRC.