No, that's almost fractally wrong.
For one, you don't need a transformer for stepping down voltage, as you can see in essentially every piece of consumer electronics nowadays. Your typical CPU nowadays runs in the 1-2 volt range, but PC and laptop power supplies and batteries provide various voltages between 3.3 and 20 V. Your typical desktop mainboard takes most of its power to feed the CPU from the power supply's 12 V rail. Yet, you won't find a single power transformer outside the power supply--the only transformers you will find on a mainboard are probably Ethernet signal transformers.
All of that is done by switching regulators, and those work perfectly fine for regulating 120 V down to 5 V as well.
Then, rectifiers really don't have a problem rectifying 120 V. Some of the cheapest diodes you can find are perfectly capable of rectifying 120 V mains voltage. In fact that works so well that almost every power supply, at least for consumer electronics, nowadays does just that: The input is fed through a rectifier and a filtering capacitor to first to procude (in the case of 120 V input) ~ 170 V DC. After that comes some sort of oscillator that then generates more or less AC from that, but at a much higher frequency, in order to feed that through a transformer--primarily for isolation, but if you have to have a transformer anyway, you might as well use it for reducing the voltage as well. The output from the transformer then is rectified again for most applications, which is a lot more difficult to do efficiently due to the high frequency and the low voltage.