Gate Takes over Control
They have to set some limit to allow the gate to have 'final' control over the flight. Otherwise there's too many moving parts and unknowns to deal with.
I remembering once I had GS snag me the last minute F seat on a flight after a rolling delay. Must have been just before cutoff. When I scanned my BP, the gate agent gave me a dirty look and asked 'how did you get that seat." I told him it was GS on the phone and he replied that my action really caused headaches for him trying to accommodate a bunch of travelers on the flights. I assume moving folks around, upgrading, and freeing up seats to clear standbys.