That's just calling a VoIP line so the caller ID comes up on a computer and loads the relevant entry from the CRM including order history, run by an experienced user.
You say "just" because the technology for doing this isn't novel. It doesn't feel like it's "just" anything when so few businesses bother to even put that much effort towards a good customer experience.
“Just” probably isn’t the right word: the tools have become easier but it still takes care to integrate all of the pieces to a smooth user experience. For example, no financial institution I’ve ever used has managed to link things that well despite orders of magnitude greater budget.
Sure, but they can’t even pass my phone or account number around. I’m not saying that the two businesses are comparable in complexity, only that nothing easy happens without someone behind the scenes working on the user experience.
For a pizza user, you can already build such a system yourself quite trivially by getting an FTP account, mounting it locally with curlftpfs, and then using SVN or CVS on the mounted filesystem. From Windows or Mac, this FTP account could be accessed through built-in software.