There is more to a SMPS than just a higher frequency. The duty cycle is also changed.
A higher switching frequency does this:
- Smaller transformer/inductor
- Faster transient load response time
- Smaller output capacitors
- Lower output voltage ripple
- LOWER overall efficiency
- HIGHER RF Noise emitted
Generally speaking, the lower the wattage for the SMPS the higher the switching frequency. The disadvantages of a high frequency, lower efficiency and higher EMI, are easier to deal with when the overall wattage is lower. But there are plenty of exceptions to this rule.
But just using the normal 50/60 Hz AC waveform from the wall does not really help you. The reason for this is that you still need to chop the waveform to vary the duty cycle of the signal going to the transformer. In the design of a SMPS, the turns ratio of the transformer gets you close to the ideal output voltage-- but not close enough. Varying the duty cycle in real-time allows the output voltage to be tweaked to be the proper value (usually within a couple of percent). Without this duty cycle adjustment the output voltage might vary by 10% or more.
But that's not all. Varying the duty cycle of what is already an AC waveform is tricky. Sure, it can be done but why? It is easier to convert the AC input to DC and then chop it than to chop the AC input itself. And there really is no benefit to keeping the original AC frequency.
Which brings us to power factor correction. Using the original 50/60 Hz frequency into the transformer really does not help power factor correction. It would still mainly consume power near the peaks of the AC waveform and not when the AC input is at a lower voltage.
At 12.5 kW, you don't want a transformer between the power supply and the fan. Even if it is 90% efficient, it's still going to create over 1 kW of heat. At this power level, go get the right fan that runs directly from the 230 V you have available.
Each AC cycle electric energy is converted to magnetic, and back again. The amount of magnetic energy that a transformer can 'store' is more or less linear in its mass. At a higher frequency, more of these cycles occur, hence the same transformer would transform more power, or the same power can be transferred by a smaller transformer.