Has there ever been or has it ever been proposed to set up a sportsbook or betting kiosks at the airport for travelers changing planes or wanting to place a last-minute bet before leaving town?
There have never been sports books or sports betting kiosks in U.S. airports. We can say that with some confidence; it's been less than eight years since sports books have been legal outside of Nevada and the Las Vegas airport has never had either.
That said, airports in states with legal sports betting like Newark Liberty International and Phoenix Sky Harbor allow travelers to place bets on their phones via licensed sportsbook apps while inside the terminals. That's getting close to retail sports betting outlets, but it's still no cigar.
There are certainly plans and proposals in some cities, including Las Vegas, to bring at least kiosks, if not physical books, directly into airport terminals. As you state in the question, the idea of "one last bet before my flight" is real, though it's been largely absorbed by mobile betting rather than requiring dedicated airport facilities.
Key obstacles prevent the implementation of dedicated sports betting spaces or technology.
Airports are usually controlled by public authorities and can involve federal property rules, which means bringing in gambling requires specific local and/or state laws and regulatory approval, with extra federal hurdles. And of course, operating staffed sports books (or even casino gaming areas, which issue we covered in a QoD last March) inside airport terminals adds complexity with security and surveillance, staffing, and floor-space needs.
Another wrinkle concerns proposals to allow in-flight sports betting. A Connecticut state representative introduced a bill early last year that would allow sports wagering on flights originating or terminating in that state. Around the same time, Delta Air Lines announced a partnership with DraftKings to offer "exclusive access to sports gambling" via its in-flight wifi portal. Delta quickly clarified that real-money gambling isn't part of the initial exploration, which makes good sense, considering that existing federal law currently prohibits gambling on U.S. commercial aircraft.
It doesn't take much imagination to see that mobile gambling is the wave of the future and eventually, sports fans will have access to online sports books from anywhere you can think of, including airports.