When deciding where to live people tend to think about cost of living and job opportunities as separate factors. They may move to one area because they can get paid a little more, but do not really think about the living costs. The reverse is true where someone takes a hefty salary cut to move somewhere so they can afford to buy a house.
When paying higher COL is worth it
I think it really makes more sense to think about both of them together. It may seem wise and enterprising to move to one of the most affordable cities to live, but what if your earning power takes a big hit? It is very possible that paying more to live in one of the more expensive cities will actually work out better financially if you earn more income as a result of living in that city. This is not true for everyone, but is something to think about.
Considerations when moving to lower COL
One could greatly increase their net income if they could find a similar paying job in a lower cost of living city. In general incomes tend to track cost of living in different regions to some extent. However, there are situations where particular professions are in high demand in other regions. When we have this unbalance people with those skill sets can really take advantage.
This is a tough decision for me that I constantly think about. On one hand you can mathematically find out, which job/city offers the best net income for you. The more disposable income you have can help you to reach your goals whether they are to retire early, travel more, or coming full circle live in a certain city that you really like that happens to be more expensive. Where you live can make such a difference in how happy you are. I think most of us could probably be happy no matter where we live with the right attitude, but certain areas appeal to certain personalities. I think it is worth paying up within reason for the place that really can add happiness to your life. Again only if this is not at such a burden that part of your life suffers to afford it, such as having to take on more hours at work and adding more stress to your life.
In conclusion it is important to weight the Cost of Living / Salary ratio when deciding where to live, but it should only be one of many considerations.