Why do commercial pilots wear military-inspired uniforms and have titles like "Captain?" Wouldn't they be just as competent if they wore t-shirts, leather jackets and sunglasses like Australian bush pilots?

Tradition and confidence.

If i were to board an airplane and observe two pilots wearing just t-shirts and sunglasses, i would truly expect for the plane to be hijacked.

Its a stigma implanted into humans brain. maybe, because of the movies.

An example: flew to Mexico. pilot appeared to be 16 years old and wore a flight Captains uniform. i was amazed at the talent this pilot had for flying this big 747. best flight i've ever had. if this pilot had been wearing sunglasses and a t-shirt, i would have deboarded the plane.

Is all about tradition and confidence.

Pretty much for the image of confidence with prestige thrown in. Airline training is somewhat similar to military training. It sounds funny, but it doesn't even feel "right" piloting an airliner while out of uniform. I had some reposition flights where we didn't have to wear uniforms as the airplane was empty. It felt funny for all of us to be in jeans and dress shirts while flying. I'm sure that funny feeling would be much stronger for passengers.

I am not sure of which glasses and jacket you are referring as used by Australian bush pilots, but many of the common leather aviation jackets (bomber jacket , A2 styles, etc. ) and the traditional aviator glasses are both of military origin. The t-shirt is just underwear although I am quite sure it was also issued by most countries military. I think one could make the argument that most mens fashion has its roots (blazers, trousers etc just about everything except Levis) in some countries military at some time.