I did this in Lima, Peru a few years back, and apparently it's pretty common, because lots of the flights from the U.S. get in around midnight, and the flights to Cusco all leave early in the morning because of issues with weather flying over the Andes, which are over 16,000 feet between Lima and Cusco - which itself is over 11,000 feet in altitude. So if you are flying into Cusco, which is the gateway to Machu Picchu, you're almost certainly looking at a 5-7 hour layover from roughly midnight to early the next morning. Also, the only hotel at or near the airport is a very expensive Ramada that is basically low end but charges over $200 a night for these typically 4-5 hour overnight stays.

There must have been well over two dozen people doing it the same night that I did.

It was uneventful, except for the janitorial crew which was navigating around the 25-30 of us with the big rotary floor waxers at around 4 AM.