I don't for one nanosecond believe that the people who don't care are getting cheaper tickets out of the deal. I'm sure the companies are only too happy to pocket the extra money.
It follows that competition is creating negative price pressure. There is no other explanation for why they don't charge more money already.
What has changed is that you get less and less convenience for your $ in coach. Most flights make most of their money on the 5 business travelers who pay 5-10x the minimum seat price the day before the plane leaves.
Any airline that pockets the fees rather than using it to lower fares is going to lose a lot of business on competitive routes.
That said I doubt they're directly making much money from people paying a la carte for assigned seats. I bet they get a lot more value out it letting them turn free seat selection as a perk to entice people to sign up for their credit card.
I think that most people care about their seat assignment, either because they want to sit near someone, or they prefer aisle or window, or they prefer to sit away from the restrooms or towards the front of the aircraft, etc.
In my opinion, the real purpose of this is to obscure the all-inclusive price of the ticket.
I long ago decided I'd pay extra for economy plus (or whatever the airline calls it) the cost isn't much more and the legroom is nice. My wife doesn't care (she is short so doesn't need legroom)
Most people care. Most people who don't pay care, too—they just can't (safely/comfortably) afford to pay.
https://en.wikipedia.org/wiki/Price_discrimination
(to be clear, there are many good reasons for caring, such as having children, any other personal circumstances, etc)