'Virtual' postdoc (in math)
In person and Skype are completely different. Writing math that you can both see becomes a challenge (in person, it's called a blackboard). I get up to fetch a book: communication is lost. Meeting takes longer than expected and it'd be nice to continue talking over lunch? Very difficult with Skype. More than two people in a meeting? Complete nightmare.

And a postdoc position is not just about talking with your supervisor every now and then. IMO, that's just a recipe for having a terrible time. You are expected to participate in your department's life. This means going to seminars, talk with people who you don't collaborate with, etc. Impossible if you are restricted to formal Skype meetings with your supervisor. Let's say you have a quick question about something you're reading. Are you going to call your supervisor about it? Or go to the office next door and ask, maybe even someone else, like another postdoc or a PhD student who works on the same kind of topic?

What you are describing is a research collaboration with someone else. You check up every now and then for status updates. It's not what most people envision when they think of a postdoc.