Earlier quoted context omitted.
I've missed maybe five or so domestic flights on "legacy" US airlines (American/Delta/United). If I recall correctly, on all but one of those I was rebooked. On the remaining one I was not rebooked; the airline tried to accommodate me but they couldn't get me where I was going in time for the thing I was going to. That being said, I do care if I miss my flight, because it's obviously a pain even if you do get rebooke…
Most US based airlines will charge you a rebooking fee however, so it’s not completely hassle free. It’s often around $80-100 USD. Southwest Airlines is the only major carrier I know that does not charge this fee.
Surprisingly, I've never been charged this fee (and I'd remember). I don't know why. In particular I don't have any sort of status with the airlines.