You post hits a problem we see often in planning, installing and supporting UPS systems. It's a multi-part problem..
Many times, what is done at new installation time to minimize the concern you bring up, is often degraded over time as additional unplanned (or unauthorized) loads are placed on the UPS leaving too little margin.
For purposes of discussion, you might find in typical large (e.g. hospital) telephone switching system room a 7 kva UPS system for the phone switch peripherals. The switch itself is running off the 48VDC battery/DC plant.
We spread the loads at the UPS distribution panel across many, small (e.g. 10amp breakers) to break up the loads so if there is an overload somewhere it will bring down only that circuit and few devices on that circuit. And, the smaller the breaker, the more difficult it is for that branch to bring down the entire UPS unless...
If the UPS overall load has grown to too close to the limit, the situation has been set up where the extra fault load will bring the UPS down. When we see this on our maintenance visits, the customer is made aware of the situation and suggest either upgrading the size of the UPS or installing a second UPS and break the load up . Ideally, we don't like to see more than 50% load on a UPS system.
The other common scenario that happens frequently is that someone plugs a vaccum cleaner, microwave oven, coffee pot, etc, etc into an outlet supplied by the UPS system and brings everything down. We suggest installing "non standard" twist loc 120v receptacles and changing the plugs on equipment authorized to be on the UPS, to make it difficult for Joe Blow to plug in unauthorized equipment.
Lastly and getting closer to your concern I believe, regarding mechanical breaker trip times, versus a microprocessor monitored UPS system (and potentially much faster overload detect and shutdown), in some UPS the parameter tables can be changed e.g. duration of overload and percentage of overload before initiating shut down. But this won't help much if there is insufficient margin.
I would suspect UPS topology plays into this also.. In many installations, we use a particular brand UPS that is ferro resonant transformer based (versus switching topology) because it is the largest kva rated UPS that can use the main battery plant 48 volt system (and thereby guarantee the phone switch peripherals will stay up as long as the switch does during an extended power outage).
My guess is a UPS that is DC powered off for example, the main PBX switch 1700AH 48v battery bank, and with the "flywheel" effect of the ferro resonant circuit vs some of the switching UPS, they might perform better with regard to clearing faults.
Maybe someone who is closer to the design and performance of equivalent kva ferro based vs switching UPS systems can shed some light on this..