If you are travelling to the United States, you need to complete an ESTA to be allowed entry. But should you take a paper copy of your ESTA?
The short answer is yes.
Even though it's 2020 now, I still do take paper copies of some documents with me, even though everything is digital these days. I have always taken printed copies of our ESTA's, but it was only at the end of 2019 when I was actually asked for it when I got to the airport. I was caught a little off-guard, but there was an airline manager stood in the airport queue before sending off your luggage, asking to see printed copies of ESTA's. It was the first time I'd had experienced it, and as I had printed copies, I showed them to him and then we were able to go check-in to our flight.
There were families behind us came without printed copies and they were frantically trying to get signal to login to the ESTA website (and for those who done this, you need passport number, application number or a list of personal details, which is no quick task to do) to show him. Now, he was accepting screenshot/PDF versions of your ESTA on your phone, but if your phone is dead, or something else happened to it on the way to the airport and you don't have a printed version, well, I don't know what would have happened.
So play it safe and take a printed copy with you.
You are legally required to complete an ESTA (Electronic System for Travel Authorization) before travelling to the United States of America. If you have not complete an ESTA before travel you will be denied access into the country. Navigate to the US Embassy website to complete your ESTA before making your Disney World booking.