It sometimes happens that members find it hard to see "where the OP is coming from", as they say these days. This could be because the experts don't remember grappling with the question from that particular perspective -- a perspective which, in the big picture, may not be not very useful. Or it could be because their specific gifts made it easy for them as students to sail through easily. So then you have threads like this one where the OP remains dissatisfied with the replies until the thread fizzles out or gets locked.
In this particular case I remember asking questions along nearly the same lines as the OP, which is why I found this pretty interesting:
tech99 said:
It was thought by most people until about 1920 that the side frequencies were just a mathematical artifact ... Carson in the USA experimented with narrow quartz crystal filters and found that the side frequencies do exist.
As a student I wanted to know exactly why and how a filter (like one of Carson's filters in the quote) would produce an output when the input is an AM carrier centered somewhere far away from the filter's bandwidth. The answer that I finally figured out was something like this...
It's easier to start with a suppressed carrier AM signal that contains
only the sidebands and no component at the carrier frequency. The thing about this signal is that its phase is zero degrees for one half of the modulation cycle and 180 degrees for the other half of the modulation cycle. If you apply this to a filter that is centered on the carrier frequency, the filter will build up an output during one half cycle, only to ramp down its output during the second half cycle as the opposing phase input drives it down. Think of a swing that is subjected to little
pushes at its resonant frequency for a certain time, followed by the same number of
pulls for the same time, and so on. So a filter of infinite Q will not build up significant output over many modulation cycles.
Now, what if the filter is centered around the carrier frequency
plus the modulation frequency? Imagine that the filter is already "ringing" ("swinging") at its own resonance frequency. This ringing output is sometimes be in phase with the carrier frequency, and sometimes out of phase. It alternates between 0 and 180 according to the modulation half-cycle, if we take the carrier as our phase reference. But if we look at the suppressed carrier AM, its phase is also alternating between 0 and 180. Thus the input can keep on driving the filter's resonances to higher and higher levels -- theoretically infinite output if the Q is infinite.
Adding the carrier frequency back to get conventional AM won't affect this output, a la superposition.
QED, sort of, I think.
I am not sure if this will address the OP's concern, but there you go.