Come on now, we all know how Customer Service in Dominican means "how can I find a problem". And if they can find a problem that means you miss your flight, better still. Airlines always oversell flights. A government requirement which people fail to meet means denied boarding, no refund, more cash in the bank for the airline and absolutely no chance of getting your money back.
As an example, Iberia in Santo Domingo insists that you show the physical credit card that you bought the ticket with but bury this requirement in an e-mail full of blah blah blah. My neighbour is a pilot for them and told me that every flight they prevent several people from checking in, no refund, because of this. It's good business, cash in the bank for the airline for not flying you.
If you rock up at the airport without the required QR code, I can imagine that the airlines will prevent you from checking in, keep your money and sell your seat to the next person. Maybe not on Feb 1st but sometime soon.
By the way if I as a Brit want to fly to the US, I need to show my ESTA at the airport before I check in, and on arrival in the US. It's not such a big ask.