I voted "depends, there are tradeoffs," but we're still here in our low COL area. Maybe ironically to you, one of the biggest tradeoffs for us is actually being closer to family in the low cost of living area. (I liked having some physical distance from the in-laws.)
We moved from an area with an average household income of about 60,000 to one with an average household income of about 25,000, and an overall MUCH lower COL. The difference in the cost of housing alone is insane. We moved from a 2bd/1ba house that was 1,800 sf to a 2bd/1ba house with 1,200 sf. It's basically the exact same layout, just more compact. Our PITI is $1550- a month less now!
If that was the only difference, it would still be huge, but there a lot of other things that make life cheaper in an area like this. The average lifestyle is different overall, which makes life feel more luxurious and also provides fewer spending opportunities. People used to call our old house "small for two people" and wonder when we were going to "move up," or ask when we were getting new cars, or invite us to expensive dinners we felt uncomfortable about paying for. Now our (smaller!) house is average for our area, there are very few overpriced restaurants, and no one feels sorry for us for driving an "old" car. Groceries are cheaper here. There is an actual farmers market with cheap veggies and $2/dz. organic eggs instead of a yuppie market with artisan breads and overpriced quail eggs. Where we used to live, a shitty American lager would set you back $6+ in a restaurant. Now, if we do go out, it's $1 draft happy hours. $1 drafts did not exist where we used to live. Oil heat used to be the only option, and we now have gas heat which along with the slightly smaller house has slashed our heat bills to something like 1/3.
With that comes the fact that there is less culture, etc. and we definitely have a limit on how long we're willing to stay here. But it's a really great situation to be in for stashing purposes.