I've been told that USPS sorting machines can get broken if non-bendable items are sent thru them. So the post office has created separate handling for thick or non-bendable items (with a slightly higher fee). I'm familiar with this problem because of hosting ATC swaps where some of the ATCs were stiff and needed to be handled separately. Since my goal was to get everything back to the players intact, I just followed USPS recommended procedures and never had a problem. (Several of the players, however, lost some or all of their ATCs by sending stiff cards to me without separate handling. The envelopes ripped in processing and cards fell out.)
My guess is that the smaller a post office is, the likelier it is a human would notice taped-on coins before they got to a sorting machine.