You can do this but it is more expensive. There are two stages: power factor correction, and the forward converter. The forward converter uses a transformer ma

You can do this but it is more expensive. There are two stages: power factor correction, and the forward converter. The forward converter uses a transformer mainly for isolation. The power factor corrector exists because the transformer is an inductive load. If you have too much of an inductive or capacitive load on a distribution network you affect is performance. You can make the power factor corrector, which does the rectification, out of active components that switch in time with the AC signal. This eliminates the voltage drop of the diodes which can be a few percentage points of efficiency and a fair bit of heat. If you didn't need to isolate the power supply you could chop mains directly but you need to manage the radiated noise. The current designs try to maximize safety and then economy and then efficiency. Coincidentally, the power factor correction, done correctly, also helps reduce radiated noise by keeping the system synchronized with the incoming power. (This is not precisely accurate but is an interesting way to think of it.)