Inrush Current Limiting Circuit - Would this work?

I came up with an idea that I think might manage some inrush current I'm trying to limit, but I'm concerned because I didn't come across this when I was searching for ways to manage inrush current on the internet. It consists of just an N-channel MOSFET, a resistor, and a capacitor. The principle is that the resistor and capacitor cause the gate voltage to rise slowly, and eventually the MOSFET opens and allows all of the current through.

As I said, I'm concerned because this seems so simple, but I didn't come across this in my searching. Is there some reason that this wouldn't work? I don't design a lot of MOSFET circuits, so maybe I'm overlooking something obvious here. Any input is appreciated. The schematic below is for illustrative purposes only, don't mind the component values.

I like it. I think there will be a voltage drop across the mosfet, dependent on how much gate drive voltage is needed to sustain the current in the load (all dependent on the mosfet specs, the supply volts and the load.. For this circuit, with no resistive load, the voltage on the output capacitor should eventually come up to the supply voltage as the gate voltage gradually decreases and the mosfet shuts off.
Thanks for the input! I built this circuit last week, and got some interesting results. It does indeed limit the inrush of current, but it also leads to weird behavior. I think that when Vgs gets high enough to allow current through the MOSFET, the capacitor discharges slightly, and then there's a little back and forth as Vgs tries to reach an equilibrium. That leads to the motor starting and stopping a few times before slowly building up speed like it's supposed to. This design works, but needs improvement.
With a 24Vdc motor across the output capacitor, I'm imagining at very low rpm during startup, the back emf from the motor would throw the output voltage up and down as current shifts back and forth between charging the output capacitor and raising the current in the motor. This would also affect the voltage across the gate as you describe, and the effects would diminish as the motor comes up to speed. Maybe a capacitor from source to gate would help smooth out the startup ?
But there could be another problem.
The MOSFET should have 600V rating, but also the Vgs should handle a big voltage, and this could be a problem.
Thanks for your input, AND your simulation. I did mention to ignore the component values in my schematic, so please disregard those values. I'm more curious about the general idea of slowly charging a capacitor to bring the gate of the transistor up to its threshold value and controlling the inrush current by this means. I should have also mentioned that the capacitor load should really be a 24 VDC fan for what I'm doing, or any capacitive load.
Maybe a capacitor from source to gate would help smooth out the startup ?
I tried this out, and it did seem to fix the issue of the motor teetering between on and off. I'd say there's probably a good solution buried somewhere in that circuit, but sorting out the proper R and C values is a bit tricky. A more experienced engineer could probably make this work well.
What your circuit shows is diode connected mosfet. The voltage drop across the FET will be equal to the Vgs threshold voltage. You also need to clamp the Gate to source voltage with a zener.

If you want a low voltage drop, say tens of milli-volts. You need to use one of these circuits. The N-channel FET will have a lower voltage drop than the P-channel FET for the same device size. The downside is that the load is not referenced to ground and may pose a safety hazard.

The P-channel has a ground referenced load and is probably better from a safety standpoint since the load is not floating at the input voltage when the FET is off.

I did not show this, but you will have to discharge the cap with a switch or bleed resistor to turn off the FET(s).