Right now I have $98 in currency in my wallet (mix of 20s, 10s and 1s), and my wallet is showing no signs of distress. Personally, I'd rather have eight 1-dollar bills in my wallet than a small pile of heavy coins in my pocket, all mixed in with my thumb drives, keys, and pocket knife. I also prefer not to make jingle-jangle noises when I walk, but I suppose some people like that sound.
Your pants make "jingle-jangle" noises when you walk with change in your pocket? I don't know what kind of pants you wear (too baggy?), but I can honestly say that mine keep my change secure enough (with the help of gravity) that as long as I'm not leaning over in some odd way, I never hear my change jingle. Ever. Only if I happen to put my hand in my pocket and jiggle the inner lining around on purpose, at which point it's me consciously making the noise on purpose.
First world problem. If your currency is "all folded and bent and deformed in any way imaginable", you're not doing it right. Are you one of those people who keep their currency all wadded up in a ball? Anyway, if you think straightening out a pile of money is a nightmare, you should count yourself lucky in life.
Nope, I have a wallet. Why would I roll my bills up in a ball? And I will admit that it seems to be relatively rare these days that I encounter a totally screwed up, wrinkled dollar bill, but they do exist. But my point really was, even if rare, every single bill that has a random creased side or corner adds up and adds to the annoyance of managing it and working with the entire stack money. Just four duds can make the whole pile a pain in the ass to work with. And I'm talking ones here; assuming you have 15 of them, of which 8 are pretty neat and the rest have random creases here and there, it adds up and can be a pain in the ass.
Also, I wish I could say that my wallet didn't get so stuffed so badly with more bills, but it does. Then again, I refuse to pay $100 for a little piece of leather to keep my plastic cards, driver's license and bills organized in. Maybe that's my problem, I'm too cheap, but either way, it doesn't change the fact that pockets come included with the cost of all the pants and shorts that I've ever bought, they work well for holding change silently and securely the vast majority of the time, and for me it's nice to be able to grab a couple of coins instead of reaching for a wallet, opening it and fiddling with paper.