Actually ALL of the carriers require passengers who can't fit into their seat with the armrests down to purchase a second seat. I was on a flight last year where a very large woman couldn't fit into her seat with the armrest down, and the flight was completely full. They asked for volunteers to deplane so they could move her around and get her two seats (she was going to be required to purchase a second ticket), no one would give up their seat, so this pasenger had to deplane. Although the flight attendents were very sensitive about it, I'm sure this woman was mortfified. Had she simply purchased the second seat in advance, she wouldn't have had the problem.
The difference is that SW will refund the purchase of the second seat if the flight is not full so there is an empty seat next to the passenger of size.
Airline seats are designed to fit the average passenger with room to spare. If they reconfigure the seats the planes will hold less passengers and the flying public will be forced to pay higher costs for tickets. The other option is to allow the larger passenger to leave the armrest up and spill over into the seat of the person next to them. Neither of these options is equitable.
The airlines all have the dimensions of the seats on their various planes on their web site. If you are unsure if you are going to need to purchase a second seat, it's pretty easy to figure out by cutting cardboard to size and taping it together, then trying to sit in it.
If you are a larger person and are flying with family--maybe your children who are smaller where you can leave the armrest up and take up some of their space, I highly suggest you fly a carrier who does assign seats in advance. In this case the chance of you being required to purchase a second seat is fairly slim at best.
There used to be a woman who posted on these boards a lot, her and her husband were both "Pooh Sized" and they used to purchase three seats and "share" the middle one. It gave them both plenty of room and was a LOT less costly than first class would have been. She also made it clear to the gate agent that they ahd purcahsed the third seat so they didn't try to seat someone between them. I thought that was very clever!
Anne