I'll start by saying that I'm self-taught in electronics, and tend to ask a lot of questions because I don't know NOT to ask them. This is one of those questions.
Consider: I have 120VAC and need 12VDC.
On one hand, I'd get myself a wall-wart transformer that puts out 12VDC and be done with it.
But why a transformer? Why not use a bridge rectifier to get DC, smooth out any ripples with a cap, a throw in a voltage regulator…say a 7812 in this case.
Why is one method preferred over the other? I assume the rectifier/regulator solution would generate a TON of heat and perhaps need a prohibitively large heatsink. Is is engineer's choice? or is there something in the physics that makes one solution is more efficient or cheaper to manufacture than the other? or are there some other crazy unintended safety considerations?
As someone who tinkers and builds stuff, what are some of the considerations in deciding to use a transformer instead of a rectifier/regulator in a project (apart, of course from the why re-invent the wheel when you can buy a wall wart at the corner store argument)?
I'd love to understand this a little better.