You should consider the difference that also exists in small power supplies to provide DC power to small appliances and devices. These power supplies, often called wall warts or power bricks, used to almost exclusively use transformers to step the 220V or 110V AC mains voltage down to something closer to what was required for the load. These units were heavy and bulky compared to the typical AC to DC adapters that are in typical use today. For example compare to the very small size of a typical smart phone charger that you have for your phone.
The difference is that the modern chargers, just like the ATX power supply although on a much smaller scale, eliminate the iron transformer and lots of copper wire in favor of using a high frequency switching technology. The high frequencies used permit energy conversion with much less transformer inductance and thus the transformer cores are very much smaller by comparison. In addition these small cores use materials that respond to the high frequencies much better than iron as a result they are much lighter weight as well.
The switching power supplies are more efficient and thus generate less heat. That can translate to a much higher power conversion capability in a given volume for the same or less temperature rise.
My first computer back in the dim past was a Cromemco Z2 rack mount S100 chassis. It's power supply looked like the picture below. That heavy duty transformer in the center was about the same volume as todays ATX type power supply. As you can guess that supply just rectified the transformer secondaries and then filtered the DC voltages with those large capacitors to ~9V and ~+/-18V. Further regulation to produce clean +5V and +12V/-12V had to be done on each plug in S100 circuit board.
The original Z2 specs claimed that the supply would provide 30A on the 9V output, 15A on the each of the +/-18V outputs. That corresponds to an estimate of about 800W of raw power for the computer.
Compare that to the typical ATX power supply for a gaming PC that may be rated at 800W.