Merriam-Webster defines random as: "without definite aim, direction, rule, or method," which based on the way airlines appear to actually assign non-premium seats on an airplane, is at best, disingenuous; yet airlines such as Spirit Air and others advertise that they provide "randomly assign" seating. The prime example of why previously non-assigned seats can't truly be random is that to treat a family of five, of which three of those passengers are under the age of eighteen and simply, randomly disperse these children throughout the plane, would not be a business model that any parent, or society, in general, would approve of. While, I am unaware of how the seating algorithm is setup to handle families, or adults, for that matter, that have booked an airplane ticket as co-passengers at the same time is actually handled, there isn't any doubt, that the airlines are well aware of those that have booked solo as compared to those that have booked as a couple and as to those that booked their flight as a family. This means, de facto, airplane seat assignments to which certain consumers such as families with children, for a savings of money, or for whatever reason, in which they didn't pay any further fee to get an assigned seat will not be randomly assigned seats, and I challenge the airlines to prove otherwise.
In point of fact, in absence of any evidence to the contrary, random seat assignments aren't actually random by the airlines; for another very obvious reason, which is some of the airlines have tier pricing on their assigned seats, which typically means that seats at the front of the plane, or an exit row, or an aisle or window seat, are sold at a premium price than seats that are in the middle and/or are at the back of the plane. This means, that the airline has a vested interest, very much so, that upon the 24-hour window commencing for passengers to check-in, that the very best open seats, especially those that a discriminating passenger would be willing to pay for, would probably not initially be included in the algorithm of random seats that a passenger could win. Further to the point, since the airlines know for a certainty whether you have or have not paid for baggage or any other extra fees which aren't mandatory, it certainly seems reasonable to assume, that passengers that have spent more on their ticket, for their baggage, or are frequent flyers of that airline, or whatever features that the airline finds most cogent, will receive a more pleasing selection of previously unassigned seats than someone that doesn't fall within that given demographic.
In America, there are so many lawyers and so many lawsuits, that it just seems as if airlines that advertise their seating as being random, will, sooner or later, have to disclose in detail and transparently, exactly how "random" those seats actually are that get assigned to passengers based on the time stamp of their check-in. The strong impression that I have is that these seats are gamed by the airlines, and they are gamed for a reason, to which that reason is to reward those that pay for extra things and/or are valued consumers, as well as to penalize those that don't. The other objective of the airlines is the hope that people notpreviously willing to "pony up" the money to buy pre-assigned seats will after consistently receiving a poor seat selections be "encouraged" to change their ways.