Let's make a concrete example. I'm from Italy, currently living abroad. The salary I was getting where I am now, was almost double what I was offered in my home country. We're told that the cost of living in Italy is also lower than other EU countries. While this is true, it isn't half of the rest of the EU.

I'm now in a situation where I could go back to Italy, but the above is one of the reasons that makes me doubt wheter it would be a good outcome or not.

This is to answer your point about purchasing power. With an Italian salary (considering the same tech job), my purchasing power there would still be lower than my purchasing power here with a local salary.

Yes, it can go both ways depending on the specific purchasing power, I never said otherwise, just my point that in many areas of Asia where factories are, people make way more than their local economy even if it might be less than the US.