I think dstillman put it best, the features that make Zotero actually useful need to connect to the internet, like fetching metadata. You wouldn't want to enter everything by hand (but you can).

I think your expectation is reasonable (a local tool will be offline when using only local resources), and it's definitely possible with Zotero (disable the automatic translator/style updates) but just not the default setting.

On a technical level, I don't think there is a huge difference between polling and maintaining a persistent connection, if the polling interval is short or the keepalives are long. The real question that I'd find interesting is why the translator/style updates must be "instant". For my use, once a day or once every few hours would probably be more than sufficient.