Why do federschwerten have a schilt, when longswords don't?

First of all, this isn't universal: there are sharp swords with a flared ricasso (schilt) and feders without.

"Feder" is very much a modern term, and broadly just means a longsword foil specifically modified for sparring. Characteristic features include:

1. flared points
2. wide edges
3. additional flex
4. blade shape that brings the weight closer to the hilt (thinner across)
5. schilt / flared ricasso

Longsword "blunts" tend to lack multiple of these features, largely because it is impossible to have thick edges with a blade geometry matching a sharp without dangerously increasing the weight. But a sword with a schilt that lacked the other features would not be a feder either.

Now on to the schilt specifically.... There are basically two things it does.

As others have mentioned it can add a small amount of protection to the hands by preventing the opponents blade from reaching the crossguard, or changing where it strikes it (Which of these it does depends on the shape of the schilt). Personally, I think the benefits of this are over sold when using decent hema gloves. The draw back of this is that, in changing where the swords end up, it also changes the dynamics of certain techniques, most notably grappling.

The second is that it allows you to put weight in the blade without adding it to the parts that will strike the opponent, allowing for handling and weight similar to a real sword without increasing danger to your training partners. As a result,, it helps create realistic feel without also creating realistic damage. This is to my mind the stronger argument for them, although there are other techniques that can achieve the same goal.

According to this site, the schilt is a safety thing, to route a blocked blade away from the fingers. Non-training weapons generally don't have them because, being larger and heavier, they already have a wider base.

The purpose seems to be additional protection of the hand and fingers at the crossguard, mainly by widening the base of the blade. The schilt could perhaps prevent an opponent’s blade from sliding down your blade onto your fingers, but the purpose does not seem to be to stop the opponent’s blade in front of your fingers; rather, the purpose seems to be ensuring that the blade is appropriately wide at the base, beside the crossguard. The wider the blade at the base, at the crossguard, the safer your fingers will be.

The swords used for real fighting tended to be slightly broader than this for training purposes or for decoration. Slim swords look very nice, but they do not tend to have the best geometry for cutting and doing their work effectively. A broader blade carries more mass, tends to be slightly more rigid, and will often cut much better than a blade might light and slim for aesthetics. “Feder” style training swords depicted in Germanic artwork from the 15th and 16th centuries often have slim blades (presumably for ease and safety of training), and a broad schilt at the base of the blade.

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A broader blade at the crossguard means that the opponent’s sword has to travel much further over the crossguard to hit your fingers, or must be wound to a sgnificantly greater angle in order to threaten the hand. A slimmer blade requires much less effort from the attacker to reach your fingers in the bind, meaning that hits to the fingers can be incidental rather than deliberate.

Therefore, the broader the base of the blade at the crossguard, the safer the sword for your hand and fingers. This can be achieved by having a broad blade with no schilt, or by having a slim blade for most of the length combined with a broad schilt at the base of the blade. The purpose of the schilt here is to broaden the blade where it matters most. A schilt that is slim at the crossguard, that flares out in a spiky fashion somewhere further along the blade, does not actually provide any protection where it matters most; a good schilt must provide breadth at the base of the blade, if we want it to be a useful and functional piece of protection for the hands.