I fully disagree, thomas.
Waiting half an hour or so doesn't do much more than help you start forgetting where the shot took place, unless you suspect a bad hit---in which case you want to let the deer sit still for several hours. Or, it'll help you bag a second deer, lol.
But assuming getting a second deer isn't the goal (and in some states it couldn't be, since it's not legal), I like to let the deer get out of sight in case it does stop running, and then listen to hear if it abruptly stops. If it doesn't, there's no reason to wait more than just a couple minutes. It takes long enough working a blood trail.