Yes
As the creator of the eham tag, I think we could use these. To me, a tag is like a Bat-signal to attract the right experts. I was surprised there weren't any airport tags yet.
And someone may be an expert on a specific airport, either by regularly flying from there, working there, by living in the vicinity and spotting there on a regular basis, or just by having developed an interest in that airport. Either way, if someone is interested in an airport, they should be able to follow that tag to make sure they don't miss a question.
I think they could also be helpful when searching. Although searching on either the code or the colloquial name would work, that would also turn up questions where a specific airport is just used as an example. Proper tag usage would solve that.
Because of course, these tags should only be used on questions that are actually about (an aspect of) that airport, not when the airport is merely mentioned but otherwise irrelevant to the question.
Counts
Here are some examples of airports and the number of questions that could use a tag.
- Schiphol eham: 6 questions, mentioned in 19 more
- Heathrow egll: mentioned in 69 questions, about half of which seem to be about the airport itself
- JFK kjfk: mentioned in 68 questions, useful to distinguish between the airport and the crash of the N9253N flown by JFK jr.
- LAX klax: mentioned in 49 questions, about half of which seem to be about the airport itself
- Singapore Changi Airport wsss: 4 questions with "Changi" in it, 34 with "Singapore" and thus useful to bundle the questions about the airport and to distinguish between the airport and Singapore Airlines
Practical considerations
Like I wrote in chat, my proposal would be to use the ICAO code for the main tag, having the IATA code and the colloquial name as synonyms if needed.
Also, as Jamiec commented, we shouldn't go Indiana Jonesing through our old questions, swamping the home page with tag edits. A few a day would be better.