More like: if you rejoin quickly it gives people the impression that leaving and rejoining is something that's not a big deal. But it is, or should be, a big deal. It's not so much about pain as about showing to Brits and non-Brits that if you leave, you can't come back immediately if you don't like it.
That's from the EU's POV. From the British POV, it's about improving the democratic process by doing constitutional change right, and showing that it's being done right. "Brexit was a mess, here's how to make a big decision that isn't a mess." That means enough time to understand the decision, as well as a debate in which the media doesn't just regurgitate disinformation.