It's not a matter of should. It's just that, on average, someone in a cheaper city will accept less than someone in an expensive city because what is too little to cover rent in some places allows you to live like a king elsewhere.

It's just supply and demand. Give 50k in a poor country, and (assuming there are enough qualified people), you will have quite a lot of choice. Give 50k in SF and people will be laughing at you. Why give 200k in the first instance when there's enough supply with 50k?