And I was wondering, why is it that an American flag, flown on the fourth of
July, a crayon colored flag drawn by my child in grade school, or basically
any first order approximation of an American flag, must be disposed of in
particular approved ways,

Who says that? There is such a thing as flag ETIQUETTE, but that
isn't a law. Some states may have laws against PUBLIC flag-burning.
What law do you think will punish you if you take the flag drawn by
your child in grade school, put it in a trash bag with a bunch of other
trash, and put it out on the curb?

but (I'm guessing here, not watching everyone) the
flag stamp that everyone agrees is the American flag, gets thrown in the
trash, dropped on the floor, torn apart, etc., and the flag police don't throw
everyone in jail or fine them?

It is likely that attempting to dispose of flag stamps, or for that
matter any other paper trash, by public burning, throwing on highways,
burning it in your fireplace, or similar actions will get you in
trouble with the police for such reasons as polluting the air,
causing a fire hazard, attempted arson, littering, etc.

Gordon L. Burditt