As a former mail carrier, I can tell you that when packages come into your local post office, a human sorts them to the individual routes. He or she stands in the middle of a bunch of rolling hampers - essentially a big plastic tub on wheels - that are in the same spot every day, labeled for each route, and they are trained to know which addresses go to which route. That person picked up a package, reads the address, and tosses it - literally tosses - into the route's hamper. Package throwing mail handlers that have been at a particular post office for a long time can sort really quickly, and some don't even have to look when they throw packages, because muscle memory knows how far and fast to toss a package to get into a particular hamper.
If you want them to know that it's fragile, it's best to write it in big letters on the same side that the ADDRESS is on. (Writing it on all of the other sides helps, but the package thrower is only looking for the address.) Whether or not the package thrower CARES that it's fragile is an entirely different story. They are also usually rushed, as none of the mail carriers can leave the post office until ALL of that day's packages are sorted to the routes, scanned as arrived at the post office, and then the individual carriers mark them off in their mail so they know when they get to a house that has a package. But as a former carrier, one of the first things I learned was that my packages marked fragile, more often than not, were at the bottom of my hamper, underneath bigger and heavier packages.
In a small post office, with a handful of routes, it might not get thrown far at all. In a larger post office, packages are thrown (literally - and that's also what it's called - "throwing packages"...as in, "Mary is still throwing packages, so we can't leave yet.") more than ten feet in some cases, depending on where that route's hamper lies. In all likelihood, the dent came from being tossed some distance into a plastic hamper.
If you want your mail especially taken care of, send it registered mail or Express. It gets sorted out completely separately, and Express Mail comes into the post office on an entirely separate truck from the rest of the regular mail and packages. Having it insured will reimburse - it does not get treated ANY differently by the package thrower.
Sorry, but it all can't be blamed on the machines. All it takes is a package thrower or mail carrier who is lazy, careless, or has a bad attitude to break a package. Most of the time, they don't do it purposely, but a package thrower and/or mail carrier who cares will be sure that your fragile package is treated differently because it is fragile. I completely changed the way I ship things after having worked for the USPS and seeing how mail is really handled.
