The isolated ground could have the same fault conditions as a regular EGC, but those would be in the faults from the outlet to the supplied device. That device/appliance/load itself could short, or the cord could fault. So it needs to be sized like a normal EGC.
I don't think the purpose of IG's is to isolate one IG circuit from another, but to keep the EGC isolated from other parallel grounds such as metallic raceways or EGC's of non-isolated circuits. You could think of residential wiring as effectively being IG because of the nonmetallic cable sheaths and boxes.
Every IG install I've seen has an isolated ground bar in the panel supplying the overcurrent devices for the branch circuit. That isolated bar is then either connected to the EGC bar or to its parent upstream bar with a conductor sized per the feeder. If you want to run a bunch of separate insulated ground conductors all the way back to a parent panel, I suppose you could do that and not use a local isolated ground bar, but to me if you put an isolated ground bar in a panel you'd better use a conductor sized per the feeder to serve that bar. If you were installing any circuit (IG or not), would you verify the size of the EGC feeding that isolated bar? I think most are going to assume a ground bar will have been wired with a properly sized conductor. Those bars can get so messy that it is difficult to see which wire is the one feeding it if they are all nearly the same size.
My final argument would be if you had a few individual #12 circuits and you want the IG (common or individual) to go back to an upstream panel with the insulated grounds, you'd be required to use the feeder raceway to keep it "with the circuit conductors". Since the feeder conductors are oversized compared to the #12 circuits, you'd need to upsize the isolated EGC's proportionately as specified in 250.122. A #12 EGC may be too small to allow sufficient fault current if the feeder to the panel is long,