Could you give an example of something you've done using this? So I can get an idea what you mean. Shadowrun contacts?
It's been a while since I played Shadowrun, but the general idea is that you can buy contacts with character points. Each contact has a different skill level and can help the PC in some way. So, in FATE, they would be at different steps on the Ladder, and they would be available to help the PCs. The balance is that if you give a PC a contact who is high on the ladder you balance it with other lower ladder contacts, or maybe a PC has more mid-range contacts. They also have a loyalty score. So your highly skilled contact might not be the most loyal guy. A really loyal contact might go with you into the field or put themselves at significant risk. A low loyalty contact won't turn on you, but they might not stick their neck out for you if someone is leaning on them.
The purpose here is to give the PC parts of the city to interact with through the people they have on their contacts list. So, the changeling might have a Toot type faerie contact they can go to in Central Park and pay in pizza. A priest might know a group of monster hunters he helps occasionally who make their base in a warehouse and owe him a favor. A private eye might know a mechanic who has his ear to the street. And so on and so forth.
That gives the PCs places to go and people to talk to. The PCs have ties to the city without you having to detail large amounts of it. Based on the adventure you write, you can tie various contacts to it, and the PCs can interact with the area around them and get pointed in various directions. So, its
like the city is fleshed out, but without all that work.
The Contacts skill is still useful, because you're reliant on the NPC moreso than the PC's Contacts skill. It's more of a way to get the PCs going out and started.