Using 12V fans with a 24V PSU
To answer your questions, these are my suspicions based on your observations:
The symptoms you observe are very likely an attempt to provide "12V" to 12V fans, from a 24V supply.  Such a theoretical attempt to provide 12V with high efficiency from a 24V supply probably deserves full marks for trying, but the designer IMHO perhaps did not think his or her way through all of the connotations of using mass-produced 12V fans.  The only purpose I can think of for the 22uF capacitor is that it should be "pumped" by the 24V pulses so that it hovers around an average of 12V while being constantly bled by a theoretical, perfect, constant current draw which would be identical for all of the millions of 12V fans pouring off the fan-makers' assembly lines (real-world manufacturers will see the problem already).  

Where the "12V" PWM circuit fails in practice, it has occurred (these are still my suspicions) from assuming an absolute belief in the supplied specifications of the ideal 12V fan from the fan manufacturers, and designing the efficient PWM supply accordingly, the faith in the specifications apparently leading to a prototype "12V" PSU design which is (and here is where we can all be sure) failing due to the simplistic PWM design.

Only ONE ideal fan with its constant, steady current, will discharge the 22uF capacitor just enough to keep it at a "ripply" charge state of approx.12V

Practical fans pouring off a mass-production assembly line, I don't believe for a minute are tested for extremely tight spec of constancy of current draw. That would never be conceived of as their prime requirement for their use.(my apologies, I am being wise after the event).

Thus my hypothesis for the natures of the observed failures in this case.

Now three suggested answers to the  question:  1- If the fans as dismantled are modifiable to run on their originally rated 12V, then do so and put a 12V regulator in the 24V feedline to them.  Use a series resistor with the regulator if necessary to keep the regulator within thermal spec.
2- You bought a 3D printer.  Just a tiny fraction of a percent more cost at the local electronics shop will buy you a 12VDC supply to run all three fans.  Wiring them in will be a breeze compared to what you have done already.
3- buy 24V fans as you suggest.  Quick, simple, elegant. I would do that.