What make you think it doesn't? Apparently you didn't perform a simulation for different input voltages.
Your specification isn't clear to me because you have posted different numbers in every inrush current limiter thread.
Charge time and peak current vary in fact with supply voltage. Peak current is roughly proportional to input voltage, so there's no problem at lower voltages. If the peak current is too high, you can change Rg1. There's also an option to use the zener diode to stabilize C charge current, but I doubt that it's even necessary. We would see clearer with a full circuit specification.
It's by the way not O.K. to use a schottky diode in place of D1, instead you should use a 15V zener.