@daveyf ,
The first question would be do you know what a choke power supply is?
More accurately would be a choke filtered power supply, with a few different variants.
Why not? Other than the cost and bulk, there is the question of whether they are the best implementation.
That said, most linear power supplies have some choke filtering, just for high frequencies.
Output of a bridge rectifier is DC + harmonics of twice the AC frequency. The choke in combination with the capacitor forms filter eliminating some of those harmonics, but the choke in combination with the load does as well. Hence, the output voltage can droop. So much for your high dollar, low resistance AC power cord.
To get enough inductance to be useful, you need a large inductance which means materials that are not great at high frequency. So at that point, do I really want the big inductor, or should I go for s smaller inductor and burn off a bit of power with a linear regulator? The best answer is always trade off the properties for the best overall implementation.