With regard to USP, you are right and wrong at the same time.
Low end UPS are offline UPS, ie the batterys only supply power when input power falls below spec, most usually have some form of surge protection in them
Better, ONline UPS feed power out from the batterys all the time, so outgoing power is also isolated from incoming, these sort out over/under power, even frequency glitches and feed out a "perfect" power
IMO its large dips that are the biggest issue, a switch mode PSU can handle varying voltages pretty well without issue, but one of the venues I work in has had issues with other desks before with power "glitches" not a full blackout, but more than a brown out, analogue desks cope fine, but digis from various manufacturers have a tendancy to freeze or crash (one decided to go full fade on everything IIRC, not pleasent), A reboot in the middle of a musical is not what you want.