By that logic, shortening the length of the circuit, would also "cause more current to flow" in to the fault. Cutting the circuit length in half, would be approximately equivalent to doubling the kcmil, in terms of impact on the available fault current at the end of the circuit opposite the source.
Besides, regardless of what size or length the conductors of a circuit are, the fault current will never be larger than what it is at the source of the circuit. Increasing the size of the circuit conductors, just decreases the fault current by a smaller amount. Given 20kA as the fault current at the panelboard where the circuit is supplied, you will not make the fault current 25 kA by installing larger branch circuit conductors. You might increase the fault current at the end of the circuit from 15kA to 18kA by using larger conductors to mitigate voltage drop, but you aren't going to increase it above 20kA. You'd have to install another source, or a motor load, that adds to the fault current, to actually increase it above 20kA in this example.