I've never heard of an airport PD using officers who were on limited duty. When the City of Reno ran RNO up until the mid-80s, there was a special class of "police security officers" who worked solely at the airport. They had just enough PSOs to fill out their schedule, and when someone took vacation or called in sick, they would backfill with volunteers from patrol, on overtime. I made a lot of money at the airport.

When the Airport Authority of Washoe County (now called the Reno-Tahoe Airport Authority) was created as a separate government entity, they had the power to create their own police department, but they didn't. I never understood why. Their "cops" displayed police livery for years, but every time they needed to make an arrest, a city patrol officer would have to respond to complete the process. Eventually, the city made the airport cops Reno PD reserve officers (with police powers only when on duty), and then later on, the AAWC really did create a police department.

Whether an airport is policed by its own agency or by another (sheriff's office, city police, state police, etc.) depends on the local situation, but the airport cops I've seen in recent years were very professional, and I know they have training and qualifications equal to or surpassing surrounding agencies. The aforementioned Port Authority of New York and New Jersey Police Department (PAPD for short) seldom has to consider an inexperienced recruit, as their application files are full of paper from NYPD and Newark officers looking for a better gig. Many are cross-trained as firefighters, and some as paramedics, as well.

Embarrassing job? Not from where I sit.