On my wood lathe I have a 3phase motor and the way you control the speed and direction of the motor is by altering the voltage and the phase of the power supplied.
A specially designed motor that is speed adjustable by modifying phase, somehow proves all other motors are same type? That motor is not inside a refrigerator, dishwasher, air conditioner, garage door opener, furnace, and washing machine? Appliance motors can be harmed when voltage drops too low. That threat was even defined by a number that was ignored.
One exception (a speed adjustable motor) proves everything else is wrong? That is disingenuous - junk science reasoning. Others should be criticizing you for posting so much intentionally deceptive logic.
Ignored numbers will be repeated. How much can a utility lower voltage when loads (ie air conditioners) are excessive? Either a utility must shed load OR lower voltage by not more than 5%. A lower voltage is problematic to motorized appliances. Please reread that paragraph to learn that and other facts that were intentionally ignored.
A UPS is 'dirty' power. If you know otherwise, then where is your specification number? Junk science and intentionally deceptive accusations are identified by no numbers.
Some numbers for this 120 volt UPS. It outputs 200 volt square waves with a spike of up to 270 volts. Remember high school math? Those square waves and spikes are a sum of pure sine waves. This UPS manufacturer also claims it is a pure sine wave output. He did not lie. He did not provide numbers that say how "pure" that sine wave" - such as %THD. He is marketing to the electrically naive who also ignore numbers.
You did not even know a brownout must be less than 5% - to not harm motorized appliances. Which internal part is protected by a UPS? Why is that list still not provided? UPS does not and does not claim to do hardware protection.
A Mac is perfectly happy when voltage drops so low that incandescent bulbs dim to 40% intensity. What internal part is damaged by a low voltage? None. Mac damage from a low voltage (or outage) is only urban myth created by subjective beliefs - also called junk science.
UPS has one function. Temporary and 'dirty' power so that unsaved data can be saved. That same power, so 'dirty' as to be problematic to motorized appliances, is perfectly good for all computers. Why would anyone spend $hundreds or a $thousand on a pure sine wave UPS when a cheap and 'dirty' one accomplishes same protection from a blackout? Again, protection inside computers (including a Mac) is so robust that even 'dirty' UPS power causes no hardware damage. Protection already inside a Mac makes anomalies - such as 'dirty' power from a UPS - completely irrelevant.
Again, leaving it on 24/7 accomplishes nothing useful - as proven by the facts and numbers you cannot provide. UPS does nothing to protect hardware - even proven by facts and numbers you cannot discuss.
OP asked if a power outage causes hardware damage. Obviously not.
Meanwhile, the OP should be concerned about a rare anomaly that can overwhelm existing protection inside a Mac and all other household appliances. This well proven 'whole house' solution costs about $1 per protected appliance (many times less than a UPS). With spec numbers that define hardware protection.