I think what you are talking about is not actually anything new or digital or weird. You should read up on
economic geography. Companies are routinely founded where it makes the most sense to found a company and sometimes move later.
Microsoft was founded in Albuquerque, New Mexico. They moved to Seattle later.
Y-Combinator was founded in Cambridge. After getting proof of concept, they moved to the Bay Area.
Aflac was founded in Columbus, GA because there was no major insurance company there. They also were the first foreign insurance company in Japan and one of the three founding brothers was a lawyer who negotiated a deal that protected them from competition for a decade, IIRC. So, for ten years, they were the only foreign insurance company in Japan. Last I heard, Japan constituted about 80% of their revenue.
These days, in theory, certain kinds of companies can be founded "anywhere" -- or, to use your term, they are location independent -- because a lot of modern companies are service businesses and, these days, a lot of services can be provided over the Internet. Industry tends to be very location dependent because you need to be where the physical resources are -- although this varies some, depending upon the specific industry.
Anyway, my point is that a small group of people getting together to found a company and then moving someplace that gives them some kind of competitive advantage seems to me to be incredibly common. You are talking about low cost of living as the draw, and this is a potential advantage.
Historically, big new businesses are often born during depressions. During boom times, you can sell just about any piece of crap. During a depression, if you are going to make money, you have to bring real value for the buck. Also, you have to keep costs low and costs are often lower during a depression.
Which is to say that low cost of living is not a terrible criteria for a place to live, but it probably should not be your number one priority either. There are any number of business related metrics that need to be met in order to succeed. Placing too high of a priority on low cost of living may be a recipe for failure and may reflect a poverty mentality and lack of confidence in your ability to succeed.
So, I say that many businesses can be founded "anywhere" in theory because, in reality, where you go can impact a great number of business metrics critical to the success of your business, such as available internet speed, time zone, availability of talent, weather and no doubt many other factors I can't begin to guess at, depending upon what you intend to do.
There is a reason Y Combinator moved to San Francisco after achieving proof of concept: Silicon Valley. So, in theory, they could have funded startups from anywhere. In practice, it makes more sense to be someplace with the right infrastructure, the right people, etc.