I wonder why people think that it is going to be a "stampede"? You are not the first person to think this. Everyone is assigned a number and lines up. Everyone just walks and gets their ticket scanned and goes down the jet way like any other flight. Weird. EDIT, Hah, I just read AngiTN's post.
I still prefer an assigned seat over SW's boarding. It isn't a stampede so to speak and it does cut down on people crowding around the gate (gate lice) waiting to jump in line once their zone is called. There is always someone new who is a little confused on the boarding process but not nearly as many as there used to be. It used to be much more chaotic but as more people have flown the airline it isn't as bad as it used to be.
There are some things I do not like about SW boarding. I have had an someone try to get in front of me, if I am say A16, the A20 person will stand in front of me. They are often clutching their ticket making it impossible to see their number. Most guest guess stand there with their ticket in full view. I have no problem saying "I am A16, what number are you?" and then getting in front. It doesn't happen often but enough for me to notice the clutched and hidden ticket.
So many people now pay for EBCI it has decreased its value. I nearly fell over when I got a B. When I first started flying SW the EBCI was $15 and I would get get a pretty high A number but as the years went by the numbers dropped.
I've also noticed a s significant number of groups now only have one EBCI and then save seats. The direct flights I fly to MCO are almost always full, especially since they cut the number of direct flights out of Philly. I witnessed more than one unpleasant conversation. If you have a family of 4 the EBCI will be $100, that gets pricey but I'd rather sit altogether.
I have been asked to give up my seat to a parent and child but I always point across the aisle at my family and say "I'm sitting with my family". It can and does happen on full flights and the flights to MCO are full of families who don't want to be split up. It is something to be aware of and I always pay for EBCI for that reason.
Prices for SW have risen sharply in the last few years making the extra drive not worth the trip. They have cut the number of non-stop flights. So I have moved to Delta out of my regional airport.
There are big downsides to this. There is always a connecting flight making the flight a little more nerve racking. The planes out of my regional airport are small and the seating is cramped. What caught me by surprise was the overhead bins are much, much too small for the number of passengers and do not fit standard carry-ons. This turns out to be a bigger problem than it would seem. If you gate check your bag you will have to wait until they unload the bag which is time consuming and nerve racking if you are running for a connection. Standing on the jet way in sub zero temperatures waiting for your bag is unpleasant. I now travel with a much smaller carry-on.