Time (in particular in a chess game) is a precious resource -- to justify spending it you need cost-benefit analysis.

Position is also a precious resource in chess. You need to structure your play so that the trade-off between time and position is optimal, and cutting off your search the moment you think of a playable move is not that trade-off. Evidence in favor:

1. I've personally competed in several mid-to-high-level chess tournaments and have an ELO rating of 1853. Every time I've ever blundered, it's been because of a failure to give the position a second look. Furthermore, I can't recall a single time the act of giving the position a second look has ever led me to time trouble, except in the (trivial) sense that every second you use is precious.
2. I have personally interacted with a great deal of other high-rated players, all of whom agree that you should in general think through moves carefully and not just play the first good-looking move that you see.
3. Lasker, a world-champion-level player, was the one quoted as giving this advice, and according to Wikipedia (thanks, bentarm), the saying actually predates him. If the saying has survived this long, that's evidence in favor of it being true.

Your position offers no criteria and no way to figure out when you've spent enough resources (time) and should stop -- and that is the real issue at hand.

Nor am I claiming to offer such a way. I agree that the optimal configuration is difficult to identify, and furthermore that if it weren't so, a great deal of economics would be vastly simpler. My claim is a far weaker one: that whatever the optimal configuration is, stopping after the first solution is not it. This may sound trivial, and to a regular LW reader, it very well may be, but based on my observations, very few regular (as in not explicitly interested in self-improvement) people actually apply this advice, so it does seem important enough to merit a rationality quote dedicated to it.