Why adulterate ports vs using an additional IP address? Was: Ports IP specific?

I hear of people using off the wall ports to support multiple listeners. I'm not talking about anything difficult to bind specific, I'm just referring to the easy stuff, like TCP/IP.
Why would anyone set up a web server on port 80, another one on port xx, another one on port yy, etc? Instead, why not just supply multiple IP addresses to the box? Doesn't using multiple port numbers like this cause one to either use some redirects, or have the end user have to specify the port in the url, like http://myserver.com:xx?
Is it because it appears to be a drudgery to talk to the network guy and get another IP address? Or why else?

Rob Berendt