Holy shit, then you are an idiot. >why did America do this arbitrary thing
That is what you are asking. Ask yourself this, without answering "because x did", why should they use coat of arms?
You are very confused. >has its own flag and seal whereas each city in the uk has a flag and arms.
You just there said the UK doesn't use seals, they fucking do, they put their coat of arms on their seals.
The seal is literally a piece of wax with an imprint only the person imprinting it owns. It's got nothing NOTHING to do with flags, coat of arms, nothin. A seal is a fucking seal. It can be anything, it can be a fucking X.