I'd say there's plenty good reason to show the full address, and further, lack of good reason not to.
If there's a demonstrable cheater or some such person on the server, why would we want to track down an admin, or grab the partial IP and hope they will dig through the logs to find the rest for us later? I don't know about the rest of the admins on my server, but I have a day job and I don't have time for all that. In the past, whenever someone would try to contact me about a problem happening on the server, I invariably only found the message some hours later, as I'd been busy while it was happening.
This is why I have bans on, weak ban reasons allowed (as the server makes poor decisions about this), and full IPs shown, so the users can ban and report offenders themselves, and it's totally hands-off for me -- I can provide half-decent servers to the community without having to be there all the time (though I do need to update my maprot at some point).
As far as why not to show the address, what reason is there? Privacy? Paranoia? Contrary to what seems to be a common fear, there is no public database where someone can use your IP address to find out exactly who you are and where you live. Someone can use geolocation to find what city you're in (and it'll probably be wrong), or guess at your general area by looking at the wire center listed in RDNS of your ISP IP address. No exact information will be had unless someone works at your ISP and is willing to get fired for looking up customer information without a valid business reason.
Look at it this way: your IP address is visible to any service you connect to (unless you're using VPN or something), which means it's easily visible to anyone who wants to see it. Even if you're not on an AC server that shows the full IP, all anyone has to do is send you a link to a funny picture hosted on a site they control, then look at the access logs.
What else is the concern? Security? As said, IP addresses are no secret and aren't meant to be -- it's how the internet functions -- so obscurity here is not security. Hopefully nobody relies on this alone, but instead keeps their OS patched (and didn't just disable the ISP's firewall without putting in their own).
If there's a demonstrable cheater or some such person on the server, why would we want to track down an admin, or grab the partial IP and hope they will dig through the logs to find the rest for us later? I don't know about the rest of the admins on my server, but I have a day job and I don't have time for all that. In the past, whenever someone would try to contact me about a problem happening on the server, I invariably only found the message some hours later, as I'd been busy while it was happening.
This is why I have bans on, weak ban reasons allowed (as the server makes poor decisions about this), and full IPs shown, so the users can ban and report offenders themselves, and it's totally hands-off for me -- I can provide half-decent servers to the community without having to be there all the time (though I do need to update my maprot at some point).
As far as why not to show the address, what reason is there? Privacy? Paranoia? Contrary to what seems to be a common fear, there is no public database where someone can use your IP address to find out exactly who you are and where you live. Someone can use geolocation to find what city you're in (and it'll probably be wrong), or guess at your general area by looking at the wire center listed in RDNS of your ISP IP address. No exact information will be had unless someone works at your ISP and is willing to get fired for looking up customer information without a valid business reason.
Look at it this way: your IP address is visible to any service you connect to (unless you're using VPN or something), which means it's easily visible to anyone who wants to see it. Even if you're not on an AC server that shows the full IP, all anyone has to do is send you a link to a funny picture hosted on a site they control, then look at the access logs.
What else is the concern? Security? As said, IP addresses are no secret and aren't meant to be -- it's how the internet functions -- so obscurity here is not security. Hopefully nobody relies on this alone, but instead keeps their OS patched (and didn't just disable the ISP's firewall without putting in their own).