Isn’t living in an area with high prices better than low prices if purchasing power is the same?

I’ve heard some people say that purchasing power is the only thing that matters. But is this really true?

Let’s say the median salary in City A is 100k and in City B is 50k. Prices in A are twice as high as in B.
Wouldn’t it still be better to live and work in A?

Here’s why:

1. You can go to vacation in other cities or countries and spend time very comfortably there thanks to your higher nominal income.
2. You can also save more nominal money and invest more nominal money.