It is true that we see a snippet of the family interactions when we see a tantrum.
But it is also true that a tantruming child is in pain- for whatever reason. Just because we dont’ behave exactly like that when in pain doesn’t mean that they will always and that they aren’t entitled to their pain.
Imagine you see something you really, really want. I wanted a Pfaff 7570 for a long time before I bought it. When I thought about it too much I felt the longing in my stomach and the joy I was being denied by not having it. I waited over a year for that machine. Could a child who has only lived for 5 of those long years imagine waiting that long for something she wants equally? Clearly not. I have learned over time to wait; children are still learning that.
Imagine your favorite person or pet in the world just fell down the stairs and they’re shrieking in pain because they twisted their ankle or they just lost a chance at the best job in the world. Do we dismiss the pain because it isn’t ours? Do we dismiss their pain because they aren’t “cute”? I doubt it. We react to their pain because we care about them. Parents react to their child’s pain- emotional or physical- because they care, and because it’s their job.
When I’m in traffic and there’s a noisy car next to me, or a jackhammer, I roll up my window. If I’m at a cafe and someone is smoking in a smoking-allowed area, I move away. When someone is harranging the salesclerk at Target, I tune them out. When someone’s child is tantruming, I offer sympathy to the parent if they’re open to it, distract the child if appropriate, or tune it out. I don’t invest emotionally in someone else’s problem and let my blood pressure go up because of it. I deal.
Interestingly, there is a store I frequent on a monthly basis and have for longer than my daughters’ lifetimes. Generally my girls are with me. When my younger daughter was about 2 she cried because I wouldn’t let her rearrange the display because it would make more work for the employees (was my stated reason). One of the employees commented to me that he had never before heard either of my children cry- and it wasn’t because I let them run wild. I like to believe it’s because I work very hard to prepare them for a situation, beit food or restwise, or expectations in a particular situation. It certainly isnt’ because I’m going to hit them or because they know I’ll stop my shopping if they “misbehave”. When a new situation comes up I explain the rules when they behave differently than what is expected of them. Sometimes they can’t comply because they are just too young, but why would I withhold the information from them just because they are too young? They are certainly welcome to ask for justification on the rules as well- I don’t feel it to be a threat to my “authority”. I just assume they want information, or a bargaining point to change the rules. 
When my Siamese cat was a kitten, we would put him outside whenever he hit the older tortoiseshell. One day he hit her and ran to the door to go out. 
That was the last time he had that means of getting the door open.