TOS doesn't make it clear whether the Enterprise is throwing away all that Hangar air, or saving it by sucking it into tanks before opening the doors. The first way wastes life support resources, and the second wastes the ship's capacity to haul around the extra machinery. It's costly to pressurize that huge bay.
Actually, it makes it quite clear in "Journey to Babel"
[Hangar deck]
(As the NCC1701/7 arrives, the honour guard smarted themselves up outside.)
VOICE [OC]: Clear hangar deck. Clear hangar deck. Depressurising. Recovering shuttlecraft. Hangar deck pressurising.
(The guard line up, holding phasers with arms crossed.)
MCCOY: How does that Vulcan salute go?
(Spock demonstrates - right hand with the fingers separated into a V-sign.)
MCCOY: That hurts worse than the uniform.
(A couple are escorted from the shuttlecraft.)
KIRK: Captain James Kirk.
SAREK: Captain.
KIRK: My First Officer, Commander Spock.
SPOCK: Vulcan honours us with your presence. We come to serve.
SAREK: Your service honours us, Captain.
KIRK: Thank you. Chief Medical Officer Doctor McCoy.
MCCOY: Ambassador.
SAREK: Doctor. My aides and she who is my wife.
(He holds out his right hand with two fingers extended, and a human woman steps forward to touch them.)
AMANDA: Captain Kirk.
KIRK: Our pleasure, madam. As soon as you're settled I'll arrange a tour of the ship. Mister Spock will conduct you.
SAREK: I'd prefer another guide, Captain.
KIRK: As you wish, Ambassador. Mister Spock, we'll leave orbit in two hours. Would you care to beam down and visit your parents?
SPOCK: Captain, Ambassador Sarek and his wife are my parents.