A Layman's Tale: Twinkle, twinkle little star

Our Sun shines with a luminosity of 1L. By the time its light reaches Earth it is already perceived as a much smaller, brighter and hotter disc than it truly is. By the time its light reaches Pluto, 6 billion km from the Sun, it already looks like any other star in Earth's night sky.

Our nearest star, Alpha Centuri (A) shines with a luminosity of 1.5L. and is 41.5 trillion km away from us.

Question: How can the light of a star, which is one and a half times brighter than our Sun, travel nearly 7000 times further (41.5 trillion divided by 6 billion) and still be perceived to be as bright and large in the Earth's night sky as our Sun would appear when viewed from Pluto?