This is certainly not a problem with XMPP now. I run my own XMPP server and use XMPP to share things between my different devices. I have multiple accounts logged in from multiple machines all day every day.

What I really like about XMPP is that I can do precisely this. Also, setting up and running prosody is dirt simple if you have any UNIX experience. IMO it's even simpler than running your own web server.

Exactly. XMPP's a little younger than AOL, but the idea of having more than one device connected to the Internet and using them simultaneously, was sheer opulence at one point. Combined with XMPP being an open protocol and difficulty incrementing protocol versions, lead to the shortcomings described.

From my memory at the time AIM and Skype would both Just Work. I think maybe MSN would forcibly log you out if you logged in on a second computer? (Still better than continuing to route messages to your other computer, which is what XMPP does by default).