The complicating factor is that it isn't just "their property", it's an essential destination of many people's ability to function in society, which makes them adjacent to public utilities. If the water retailer which services your home started adding substances which could be used to track and identify their customers, you'd be pretty unhappy. Private ownership doesn't absolve an entity from public accountability, especially when there is extremely little option to not engage them.
> The complicating factor is that it isn't just "their property", it's an essential destination of many people's ability to function in society
That's a much bigger can of worms, one that reaches well beyond just airports. Many modern societies are extremely complex and assume individual access to a long list of resources and services.
Its a pretty slippery slope though. People can absolutely choose not to fly, it isn't a basic requirement for life. The slippery slope leads to larger and larger government - as long as society continues to create implied requirements on the individual it seems reasonable to give more and more power to a central authority to ensure everyone can have that access.
It sounds reasonable enough, though there isn't a good guardrail built in to avoid eventually building a totalitarian or communist state as so many things are now " basic necessities."