Airports have massive queues, much larger staff numbers, far larger waiting areas and even a very busy airport doesn't have the same number of people that some of the tube stations deal with per hour.
Unless you're expecting people to arrive at the tube station several hours in advance of every journey and massively enlarge them it's not practical.
Heathrow (one of the busiest airports in the world) has something like 800k passengers a day, the London underground deals with around 5 million many from smaller stations that aren't even fully manned.