I'm not a developer, so be careful with my assumptions!
You are right in that technically the wallet (if we should call it like that) doesn't need to be running on the same machine and can be accessed via web-browser from everywhere, BUT:
I don't think it is safe to run the NXT Client on a server for now, because either the passphrase or the private key might be transferred to the server and you don't know who is watching it. HTTPS is encrypted until the server is reached but from that point someone could easily log your data.
Another vulnerability might reside in the server itself, as it keeps a session for you. As I don't know the implementation it could be possible to hijack that session and at that point someone could transfer your funds even without knowledge of your password and private key.
I could be wrong in both cases, but keep in mind that the NXT-Project is in development and not even officially launched yet and nobody except the developers know the details. In general it is easy, inside my LAN I have it running on the server and can connect from every computer at home. I trust the network but I wouldn't trust the internet. If you do, be careful. I would wait until it is reviewed and considered stable and safe.
--mono
