It would be even more accurate to say "Many power supplies, especially when computers were much less power hungry, had enough capacitance to be able to survive

It would be even more accurate to say "Many power supplies, especially when computers were much less power hungry, had enough capacitance to be able to survive 0.1 to 0.2s needed for the operator to reset the switch back on. This only works when the switch is switching AC and the motherboard stays connected to PSU. Since ATX standard was introduced the switch actually disconnects the motherboard from the power supply and it is no longer possible. Many power supplies still have independent AC switch but this is not typically operated by the user to switch the machine on or off."