I fly Delta routinely. 9 flights in 18 months. Never had this type of problem. I missed a connecting flight, they directed me to a courtesy phone and got rebooked on the next flight (showed up on my smartphone as we talked). No extra charge since we departed late from my originating airport.
Love their app. I get text messages confirming my luggage is on board my flight, get directions through airports to connecting flights.
I fly coach, and the only exception is if I cannot get an aisle seat I will buy two seats (still cheaper than first class) so some lardass doesn’t push me out the window.
I take about 100 flights a year. It is not a big deal to be moved in the same section or class. Moving someone down to a lower class after being boarded and seated is pretty rare. Almost nonexistent. I personally have never seen it unless it is so done who was complimentary upgraded and required to return to their originally booked class.