I think the more predominent reason is that home computers and home connections are rarely (or never) equal, or even close to, those that ISPs can provide. What's more, leaving your computer on all the time is not what they mean by a 24/7 connection.
One example would be that, in the UK at least, the fastest home user connection you can get is 2mbps (and that's quite new) - to link a server to DALnet in the UK you need at least 45mbps (T3) and it must be dedicated to the server alone.
99.9% (as I am not exactly an expert in this I don't say 100%, but it's probable) of computers will not meet those requirements, so networks simply say "no home computers" to prevent tedious, boring applications that aren't even worth looking at.
Best of luck with your IRC network