When you are boiling food in a pot of water on the stove the important goal is not boiling the water. As you point out it's easier to boil water at high altitudes than at low. The goal is normally to increase the temperature of the food. This allows the desirable chemical, structural and sanitary changes you are after to take place.
For instance, if you are boiling an egg you want to get the insides to coagulate. If you are cooking spaghetti you want to get the liquid water to hydrate the starches. If you are frying chicken you want to get the internal temperature up to an appropriate temperature to kill bacteria.
There are some cases where boiling away water is the intent, but that is the exception rather than the rule. Thickening sauces is normally done with starches or eggs, not by desiccation.