Pleasantries from a captain with no control of any other flight aside, if you're not at the gate 15 minutes before posted departure, you've missed the flight, regardless of any circumstance that leads to the aircraft sitting at the gate for a few minutes after door close. UA actually has some industry leading tech in ConnectionSaver to systemically consider holding flights for connecting pax, so it's not being done on an ad hoc basis. Proactive rebooking certainly isn't an industry-wide practice (some major airlines don't even have the tech for it), but UA has the best capabilities for self service in the mobile app of any airline I've ever misconnected on.
Wow, I really sound like a UA apologist, maybe it was the hyperbolic tone of OP that got me going. Fault UA for where they're actually bad (cleaning, catering, etc), not for sort of normal travel stuff.
We flew UA to/from KOA during the various west coast storms this month with no drama, other than the underwhelming facilities at KOA.