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.