You misunderstand. Kyuubey has spent significant amounts of time to convincing Madoka to contract, which suggests there was something different about her even before ramping up her potential got involved
This is false.
In the first few timelines, the ones before Madoka's potential reached the current state if being more desirable than the possibility of keeping the system working, Kyubey didn't spend a significant amount of time to make Madoka contract.
Because absent Homura intervening, Madoka contracts as soon as he shows up, to save a kitten that was just run over by a car.
It's only after the timeline where Madoka asks Homura not to let her wish anymore, thus after her potential is already considerable, that she doesn't wish right after meeting him and thus he has to insists.