It sure must be nice to be one of those New York guys able to foresee the future and know that you'll never need more than 3 rounds; you'll never get lost, never encounter a situation where there is any chance of a threat, or never have an opportunity to miss your shot for any reason and have to fire 2 or 3 or 4 more.
Most guys spend some time and money to pull together a week long hunting trip. Like others have said, ammunition is relatively inexpensive and not very heavy, and to have a hunting trip end unsuccessful or worse due to running out of bullets doesn't seem like very wise planning to me. Then there are also the 'low probability/high consequence" scenarios...
Low probability/high consequence can be applied to many things: Survival, lost animals, or even failed self defense attempts. One that comes to my mind....
Last year, I was flamed pretty nicely for explaining how an antelope ended up with 5 bullet holes in it (the subject was even referred to several times in several threads after the original).
It was one of those unfortunate situations, where no matter how much planning, preparation, and practice goes into the first shot... Everything just falls apart.
A misjudged shot, and mistake with ammunition caused a fatal wound to the antelope, but it was still very mobile (and showing it by hitting 45+ mph). So, three hunters went into "salvage mode", stopping at almost nothing to stop the goat (which would quickly be lost). We would rather have massive meat loss, than have a wounded animal get away. In the end, something like 12 shots were fired, and it had 5 wounds in it (ended up being two chest shots, a head shot, and two that wasted almost no meat). It was far from a proud moment for any of us, but we were glad we kept the animal from escaping to suffer a slow, painful death.
It's not a common occurrence, and not something any good hunter thinks they will ever have to deal with, but terrible situations do arise out of even the smallest mistakes.
Taking enough ammunition to get the job done is never a mistake. Taking a minimal amount is just an invitation for disaster (unless you're unethical, or arrogant enough to think it'll never happen to you).