I'm not egregiously overweight. I'm just a large man. 6'5", 250 lbs.
Coach class on some airlines (hello Delta) is like torture. My knees press against the back of the seat in front of me, god forbid they recline it. My shoulders are so wide (and I'm not giant that way) that if I sit besides another person who is not "challenged of stature", there is not room for my shoulders or arms. I will almost always pay for "premium economy" to get the leg room, but there is still the matter of fitting my shoulders in. My butt fits in the seat just fine, it's just that my butt is not the widest part of me.
I'm all for smaller seats for smaller people. The airlines can fit them 10 abreast for all I care. But I feel bad for the person sitting next to me, because I am wider than the seat is, and it is not because I am overweight.
On the last flight I booked, premium economy was 24% more than coach, so it's not as cheap as you claim. I cannot afford first class for personal trips. First is usually 2.5 times the price of coach. I'm just an engineer.
Also, the width of shoulders of the *average* American man is 18.5" -- quite a bit more than the 16" seat width that is typical in most airliners. Do you want to jockey with me for that 2.5 inches? I didn't think so. If you have not noticed the silent battle for the arm rest, I'm guessing you don't fly very much. Seat cramping is a problem on most airliners.