The short answer is because you would otherwise have the calorific needs of hundreds if not thousands of men depend on circumstance.

I will be mainly talking about the High and Late Middle Ages in the Netherlands here. In this locale living off the land is less ideal than it sounds, and becomes more and more problematic the more troops are involved. In an earlier answer I alluded to the 1345 siege of Utrecht and the alleged numbers involved, as well as the amount of liquids and foodstuffs that was required (and purchased) to sustain these numbers. If we assume a man on campaign needs 0.5 litres of beer or wine and 1 kilogram of food a day to sustain himself, fielding a force of a 1000 men would already require 1000 kilograms of food and 500 litres of liquids a day. This is an impractical amount to forage in this area with limited crops available in comparison to the density of the population, let alone doing so for larger numbers.

There's also the issue that being dependent on the land or - what was often the case - on local farming, is inherently risky. There are no guarantees there's any food available to begin with. If the enemy knew you were coming (and because of the way troops were mustered as well as the short distances in this locale, they often did) chances are most of the crops would've been harvested (even if that meant doing so prematurely) and livestock would've been driven to safety.

This is not to say foraging didn't happen. We know it did. Sometimes there was no alternative, such as when a force was cut off from their logistical apparatus. But more often than not foraging is just a wonderful addition to your own logistics; not only do you get something extra for your troops, but you're able to damage the enemy's infrastructure at the same time. The situation could be remarkably different in other areas however. Perhaps others are willing to speak to that.

EDIT: I edited the above answer to specify it towards the Netherlands.

I think the key thing to say is that armies generally did live off the land in one way or another. The way you've conceptualised supply lines isn't how most logistics, particularly pre-1900, worked.

Before the introduction of the automobile, the vehicles available to an army, i.e. horse and other animal-drawn carts and wagons, do not have an appreciably greater speed than marching men, so couldn't really catch up to a moving army anyway. That means that it was not simply impracticable, but indeed all but impossible to use wagons and pack animals as a way of shuttling supplies from depots behind the lines up toward a moving army. Instead, the wagons and pack animals were part of the army, and more often than not were carrying supplies that the army picked up along its route of march. This could be by pre-arranged agreements with local leaders up ahead (allied or otherwise), by having established depots in advance in your own territory, by having money set aside for purchasing supplies at markets, or by taking the supplies by force or with the implicit threat of it, or any combination of the above. And in a few cases, armies attempted to load up all their supplies before setting out, particularly in long stretches of terrain without supplies.

The 'long or otherwise difficult to move' chains of vehicles and pack animals were, therefore, not in fact shuttling supplies from rear bases, but directly accompanying the army to expand its carrying capacity. Keeping the wagons from being lost was important for many reasons, including the fact that they were carrying an army's current supplies – especially useful if you ended up having to retreat and would be going back through territory whose reasonable surplus supplies you had already exploited.

Speaking of having to retreat, the term 'supply lines' ends up being colloquially conflated, quite often, with another, more consistently important phenomenon, that of lines of communication. Lines of communication are the routes that an army has leading to and from some sort of original base. The line of communications is important for a few reasons: firstly, as the name suggests it is how an army stays in contact with some kind of central authority; secondly, it is how it may receive reinforcements and extra supplies, particularly those unavailable in the theatre of campaigning; thirdly and arguably most importantly, one or more such lines may be an army's line of retreat to get out of a situation. These lines of communication were not the be all and end all of an army's logistics, but they still had immense importance in other ways.

That's not to say armies never brought supplies up from the rear, but it is to say that particularly in any pre-modern context, a 'supply train' was actually the army's moving inventory space, rather than a replenishing supply source.