I would call my use of bangs getting to a specific page on another site rather that searching another site. For instance, I get a lot of use out of the wolfram alpha bang, !wa, in those uses I'm not searching as much as I'm inputting a calculation for wolfram alpha to perform and the bang let's me skip a step by typing "!wa {quety/calculation}" into my address bar. Similarly, if ddg is your default search engine, you can lookup a url on archive.is just by prepending it with "!archiveis " in the address bar.