No, you did pick your seat when you boarded, and it worked just fine for 50 years.
When you checked in, you got a boarding group (A, B, or C) and a number, 1-60. You weren’t assigned a seat, you lined up to get on board in order, and took whatever seat you wanted.
Families were permitted to board between groups A and B, so they could all sit together.
SW did this because it had been proven that open seating was the fastest way to fill a plane. (Mythbusters demonstrated this in one episode.) This allowed them to tighten their schedules by completing the boarding in 30 minutes instead of the 45 or more other lines took, and get more flights in a day.
Some people didn’t get it, but I thought it was great, and it made me (and lots of others) loyal to SW for decades. Until this year.