Let's see, I'll take a crack at this. The first thing you must consider is that your question covers a period of thousands of years so a lot of this will be necessarily vague and generic. With that in mind...

One of the biggest problems in warfare is feeding and equipping an army. When you get 10,000 men together you can't just walk into the local market and pick up what you need. So most armies historically have had to deal with that. There are basically two ways to feed an army. The first is to split it up into lots of little groups and have them roam the countryside requisitioning or stealing what they needed. That of course splits up the army and leaves it very vulnerable to counter raiding.

The second solution is to set up supply depots and delivery systems. These supply trains had to be guarded. So you still have to split up your army, but it's in more controllable and larger packets. So whenever you have a more organized state you usually had some sort of organized supply train. Even for an organized state it wouldn't be uncommon to still have foraging parties as well. The Battle of Gettysburg was famously started because some Confederates were looking for a supply of boots.

In any case regardless of supply situation, armies have always been vulnerable to raids on their supplies. An army can break up and raid their opponent's supplies and destroy an army without directly engaging it. Imagine two sides with 1,000 men, but one side has divided into 10 companies of 100 each. If the 1,000 man army catches one of those companies it'll destroy it. But each of those companies is easier to feed, and more mobile than their opposing force.

Now if you put each of those companies into a fortified position you've given them great tactical flexibility. Sure the big army can take any of the forts. But that takes time and effort. While that's going on the other companies will be free to act while the big army is dealing with the first company. They can raid supply lines, take out small foraging parties, and can run back to their fort if the big army turns to face them. Should a good opportunity present itself the smaller forces can combine and suddenly turn into a single larger force capable of taking on their opponent directly.

Let's turn this into a real world example. During the American Civil War a group of Texans and New Mexico volunteers led by Henry Sibley tried to wrest New Mexico from the Feds. The Feds had a larger army, but it was split in two in well separated forts. Sibley hit the first army and beat it in the field. So they retreated to Fort Craig. Fort Craig had a large supply depot leaving that army with a year's or so of supplies. Something the Confederate army didn't have. And while the Confederate army was big enough to beat them in the field, it wasn't big enough to closely invest Fort Craig. The army there could still get communication and supplies. Nor did Sibley have enough men to assault Fort Craig.

So Sibley turned north to try and take out Fort Union. The army there also came out and met the Confederates at Glorietta Pass. The Confederates beat that army as well, driving the Feds back. But the Feds also found the Confederate baggage train. They grabbed what they could and spoiled and burned what they couldn't, killing or stealing 500 horses and mules.

Sibley now had a real problem. He had two opposing forces. He had beaten both of them, but combined they were likely stronger than him. Both were in strong, well supplied positions. He didn't have supplies to besiege either of them. And he didn't have enough of an advantage to be able to hope to be able to storm either. On top of that reinforcements were coming in from California and Colorado. He was likely going to be outnumbered by at least 4 to 1 very shortly. So he did what he had to and went back to Texas. The forts had provided protective regrouping points, protected supply caches and gave the Fed forces time and space to outmaneuver and outlast their opponent. They acted as force multipliers.

Similar campaigns can be seen throughout history. Forts give armies time and strategic flexibility. They provide prepared battlefields against the aggressor foolish enough to engage them. They provide an ability to shape a campaign. One of the most important things the Great Wall of China did was to make some passages so difficult, it forced invaders to go through one of several key passes. Instead of having to guard 1,000 miles, they only had to watch 1,000 miles and guard a dozen.

You are right that a large fortress could spell doom for an army if it got trapped in there. However a such an army would likely be doomed in any case. If they couldn't win in a strong defensive position with supply stores, they were unlikely to win without them. In a strong position, additional armies can be raised, the besieger can be waited out, and if a besieger turns to spoil other lands, you can turn on them and hit them in the rear while they are occupying your other valuable lands.

/u/QuickSpore has already replied with good factors. If I may add a few more factors?

"proceed to siege you, just waiting out your supplies" has some assumptions.

It might be impossible or difficult to besiege a particular place due to geography (does it have sea access? are there sometimes enemies about who can break through and bring supplies?). I think that Pembroke Castle held out for several years during the Wars of the Roses. Berwick held out 7 years, intermittently besieged.

If your seige force is much smaller than the garrison, it may be possible for the garrison to sortie and crush it. So if you mask the fortress with part of your force and try to seize other properties with more of it, you might find yourself being defeated in detail, as with QuickSpore's example of dispersed companies.

So if there's a large garrison, your besieging force would have to be comparable ... but those troops are not off "occupy[ing] all of your other valuable lands".

Also consider that, in wars overall, illness killed far more troops than combat. The garrison is housed indoors, be it houses, chambers in the castle, or even castle yard huts. Especially if the defender made a point of destroying their own countryside -- and a prudent defender with time available knew very well to do that -- the attackers are mostly or all in tents or other rude shelters. The garrison's supplies are indoors. The attacker's supplies are brought via supply lines, which might be interrupted, and then stored more or less outdoors.

(By the way, supply lines for an attacker are more expensive than normal gathering of supplies by a pre-attack garrison.)

There was also the assumption of "your entire army sitting in this huge fortress". That might not be the case. You might, as QuickSpore suggested, have other units who could come after the attacker's supply lines. You might have forces of your own, or an ally, who could come break the seige, as almost happened to a besieging Julius Caesar at Alesia, or to the Third Crusade, whose army besieging Acre were themselves besieged by Saladin.

In addition to the already good posts it can also simply be stated that a fortress is a strong force multiplier, even if you disregard its advantages for housing and protecting supplies (not saying those factors should be disregarded, because they are very important, but for the sake of my post they can be).

Even a small, wooden fortress on a motte (flat-top hill on which the fortress stands) can be a substantial obstacle without proper siege equipment, and can let a defending force defend against many times their own numbers.

If you increase the fortification to say... a stone castle with a proper gate-house, and maybe even a decent moat or other impassable/near-impassable terrain features you might be able to defend against ten or twenty times your own numbers (again unless the attacker has proper siege equipment) without breaking a sweat.

With a force multiplier like that it often takes considerable effort for an attacker to bring down such a fortress, either in fielding a much larger army, or in fielding expensive/complicated and time-consuming siege equipment, or simply a lot of time to maintain a siege (and the complications of that has already been highlighted by the others). As the others have said you can't ignore the fortification however, because as soon as you turn your back on the fortress the garrison inside can start harassing you or maneuver to gather with other forces.

So even though fortresses were terribly expensive to build, and even more so properly walled cities (like Constantinople, Paris, Vienna, or many other examples), they were in the long run a very good investment simply because of the force multiplication factor and time delay imposed on an attacker.

Even if you are taken by surprise and only have a small garrison it will take days at best, and easily take weeks for a proper army to wittle down the defenses enough and prepare equipment to mount an assault, and in that time armies can be raised or gathered to threaten the attacker from outside the siege. Thus a large standing army isn't needed for "just in case"-scenarios, but you can settle for having stored up weapons and armour in your fortresses or monetary reserves to hire mercenaries, and still you are able to effectively defend yourself.