The ESTA approval process is changing soon and this will remove instant approvals of ESTA applications. Certainly if one discovers in the airport, say one or two hours before check-in closes, that they have no ESTA then it is very unlikely they will travel on that flight as the approval process will not be completed in time.
CBP press release, 11 December 2018: https://www.cbp.gov/newsroom/national-media-release/cbp-reminds-travelers-allow-72-hours-esta
Due to changes in ESTA application processing, real-time approvals will no longer be available. Citizens of participating Visa Waiver Program (VWP) countries traveling to the United States are strongly encouraged to apply for an ESTA at the time of booking their trip and no later than 72 hours prior to departure. Applicants who apply on the same day of their flight’s departure risk not having an approved ESTA prior to their scheduled departure. International travelers without an approved ESTA will not be authorized to board their flight.