Most of the published research I've read that recommends a drinking pattern like this doesn't really go into detail as to "why" it's recommended, but I'm still searching for more info because I'm curious. That being said, I feel that waiting 30 or so minutes after eating does help with satiation, but that is what I feel. I have no idea if other people feel that way, or not.
I have also read that not drinking immediately after a meal may help avoid stomach stretching since drinking too much too fast may fill up behind food. Again, I don't know if that is really accurate, but it seems possible.
Like anything, if you choose to follow it, after a while it becomes a habit and it's not really a big deal.
I'm not militant about it, especially drinking before a meal, but I usually, but not always, wait at least 30 after, but admittedly, sometimes it's more like 15-ish. If I do drink right after a meal I just sip a little bit. It can get uncomfortable really quick if you drink too much too quickly anytime, but especially after a meal. The experience can vary from person to person, of course.