I agree that it feels wrong. But at least Elaine Chao has experience in her field. Unlike a lot of other Secretaries (ex: Perry has no experience in nuclear, yet is in charge of the Department of Energy / National Labs / Nuclear program. Ben Carson is a medical doctor, but was placed in charge of Housing and Urban Development. Etc. etc.)

Elaine Chao actually worked under Bush as the deputy Transportation Secretary and Chair of the Federal Maritime Commission. She actually knows a thing or two about how this country moves (at least how it moves stuff in the Oceans). I think her words hold more weight than a lot of other secretaries right now.

Chao's history of Maritime Transportation -> Transportation Secretary at least makes sense. Maybe its not the airline experience the country needs for this specific crisis right now, but its at least a valid set of credentials for her position.

EDIT: It should be noted that Chao was voted into her position with a Senate vote of 93 to 6. For the most part, the country agrees that she was a fine pick without much controversy. She's probably the least controversial pick in all of Trump's cabinet.