In any airport I frequent, this would not be worth the money. Some garages offer free parking for 30 minutes for pick-ups, but by the time you park, go through security, eat, and return you would owe at least $4. Then there's the time/gas cost of getting to/from the airport. Even if you used public transport it could be expensive, it's like $16 round-trip on BART from SFO to downtown San Francisco.
It's really not a problem for places with decent public transportation. There are parts of the world where it makes sense to have a monthly or annual pass. I've no idea what it is like in the area where this occurred though.
The Skytrain in Vancouver goes from the downtown to YVR in about 30 minutes. It is possible to go to the airport and back on a $2.75 ticket (on weekends and holidays; the ticket is valid for 90 minutes).
I don't specifically know about Xi'an, but I remember in 2012 subways in Beijing were a flat 2 rmb (about 0.35 USD) and in Shanghai something like 2 to 4 rmb depending on distance. Nanjing was similar, but I don't remember the specifics. So assuming all Chinese cities that have subways charge the same order of magnitude, this loophole would have indeed been valuable.
There are airports that are easier to get to (for example London City Airport that I use often) - though not sure how many airports that conveniently located have good first class lounges. But would definitely make sense if you live near the airport, or work at the airport, or if rather than going just for a meal you use it as office space (go there, eat breakfast, work using their free wifi, lunch, etc.)
The city my sister used to live in had a free airport bus. Took you there for free. Might have been run by an airline. Saw many flight attendants utilizing it.
