Why do store-bought dips have such a limited shelf life?

I would assume that it's for safety reasons.
Not yours only, but the manufacturers' as well.

At the plant the manufacturer can control the environment and make sure that the product leaves in a condition that should last for a certain time under specific conditions ( e.g. when refrigerated). Subtract a bit for safety and you have the manufacturers best-before-date.

Once the consumer opens the sealed package, all bets are off: There is no way to know what may be introduced into the product. This may be as simple as getting oxygen to food that was sealed with packaging gas, introducing new (and ever-present) bacteria, yeasts or mold spores in a previously pasteurized pack or simply scooping with a not entirely clean spoon. Leaving bread crumbs or double-dipping is simply a very extreme example. In other words, one never knows what might start to grow after opening.

But if the product is refrigerated promtly and consumed within X hours, it may be assumed that even if something risky was introduced, the time/temperature is too short for it to multiply into a critical amount leading to foodbourne illness.

If you work very cleanly, I assume that you could extend this time frame quite a bit, but obviously won't tell you to do so - lest you or some other reader comes back complaining that I told you to and made you sick.