A very creative idea, and something I'm surprised never did show up in Star Trek. While there were references, we never did see the equivalent of passenger ships much less airplanes in the series.
I suppose the Pan Am appearance in 2001 may have caused them to avoid that idea.
Most of the cargo ship references were more along the lines of "tramp steamers" than luxury liners / airplanes. You could transport cargo or raw material - I believe the Charlie X featured an ore carrier. And those ships could and did transport passengers.
I agree that they must exist. In a way it is a shame we never got to see more of them. It would have opened up several new story areas for the Enterprise to have been seen.