That being said, I do care if I miss my flight, because it's obviously a pain even if you do get rebooked!
At least I'm usually sat in a comfortable lounge for the extra time, and can get a few things done, or just relax and read.
I recall connecting in Vancouver with Air Canada and asking the same and the answer was “thatll be $130 to change your ticket”. This is with a half empty flight leaving in 30 min.
I know United started charging some fee for last minute flight changes, but it’s way better than other airlines.
They kinda like it when you do this: it gives them more flexibility. Better to keep the later flights in the day emptier just in case there’s a sudden need. And reduces their chances of owing you compensation.