Am sorry, the discussion went off the topic, but no real simple explanation about my question! I would have expected the answer on the lines of - suppressing high harmonics is easy etc ... but there aren't really good technical answers apart from a few vague experiences.
With a conventional power supply, the transformer has to run at 50 or 60 Hz, and the smoothing capacitor runs at near the output voltage.
With a switch-mode power supply, the transformer can be run at 20 - 100 kHz, and the smoothing capacitor runs at near the input voltage.
The amount of iron and the number of turns of wire on a transformer depend on the the voltage and the frequency. At 50 or 60 Hz, a small transformer will need maybe 2000 turns of wire and will weigh maybe 50 grammes. If the frequency is raised by 1000 times, there will be maybe 100 turns of wire, and the transformer will weigh 10 grammes.
So a switch mode transformer is much smaller, lighter and quicker to make, but is much more complicated to design and to design a circuit for.
The capacitor will be physically smaller and cheaper when smoothing the higher voltage, but lower current supply. On a normal power supply, the capacitor has to support the output for nearly 10 ms on 50 Hz (nearly 8.3 ms on 60 Hz) so the voltage will drop while it is supporting the output. On a switch-mode supply, where the regulator efficiency doesn't vary a lot as the supply varies, the efficiency stays fairly good for the whole cycle as the capacitor discharges and charges. On a conventional power supply, the regulator efficiency varies as the voltage changes, so in order to allow for the smoothing capacitor to discharge each cycle, the regulator has to be less efficient.
So the trade-off is complicated design, cheap manufacture and good efficiency or simple design, expensive manufacture and poor efficiency. Where millions of items are being made, cheap manufacture and good efficiency are important. Where a hobbyist wants to make one, simple design wins. Conventional transformers also have the advantage of trivial circuits on the high-voltage side, so far less risk of a shock when fault-finding.