Chessie uses an online system.
However on our recent visit we had to split up the usage between the group as you can't use Parent Swap in conjunction with it. We had 2 people who qualified for it so used it separately in twos unless we could all ride together with baby.
Not all who use it abuse it in the manner that many unfortunately do. However it is not helped by the poor implementation of the park's own rules by many staff members. Even at Chessie there were a number of times we weren't scanned for various reasons (including not having a scanner at one of the rides).
The system exists, and they'd be better off implementing it across all the parks asap. However I don't think it'd necessarily improve things due to the number of overall users. And any methods they'd use to alter things would no doubt result in an outcry (likely from those who've happily been abusing the "free fastrack" for years); be it max 1 carer, limiting use or being stricter with giving it out. Presumably Nimbus was meant to improve matters but don't think it's made much difference.
End of the day majority who use it have to suffer with a daily issue that affects them constantly and living in an often inaccessible world. That's far more unfair than getting a slightly higher ride count over able-bodied persons. Its just a shame that many abuse the system so that those who need it often suffer and often get the "WeLl ThEy QuEuE fInE iN a HoUr RaP qUeUe" comments.