No you couldn't.
In my example, seats must be assigned. You can't seat people safely in an airplane without seat assignment.
You can assign it as an airline, or you can let the customer assign.
Not all customers care about assignment equally. Thus there is a market. And in a market you allow people to trade their value.
Pay more for preferred seating, or pay less and accept random seating. Both groups win, total welfare increases. Group A values seat-assignment more than money and gets the more valuable of the two. Group A values money more than seat-assignment, and gets the more valuable of the two. It's a classic trade scenario where both win.
The airline merely functions as the marketplace to allow people to trade, and to get to a more optimal scenario (pareto improving) where the total utility/welfare goes up.
Random seating ensures that everyone makes this trade, and thus ensures you get the closest to max pareto efficiency.
Without random seating you'd get the free-rider problem: those who don't care (or care only a little) about seat-assignment, don't get a discount that they value more. These people are not paying for a feature they don't value, and subsidise those people who do value it and are willing to pay for it independently! While those that care a lot about seating, aren't guaranteed the seat they want, despite wanting to pay for it. This decreases total welfare, it's a destruction of value.
Your punching example is different because it's introducing a harm for everyone. Everyone cares about not getting punched, it's below the baseline service. The baseline service is a ticket to safely go from A to B. Seat assignment is an extra feature above the baseline that some want to pay for, and others don't. Not getting punched in the face is a deterioration below the baseline, it's a nonsense idea to introduce it. That's why it's different. I
Of course the market mechanisms will work just the same, that's certainly true. But the morality or logic behind the airline introducing this is completely different.