That's a very harmful assumption to make. If you need a datapoint, I work remotely, and I always work at my "Bay Area" rate even though I've never lived there.

There was a point, early in my guy-on-the-beach-with-a-laptop era where I would cut my bill rate in half while working from the beach with a laptop. Clients were happy about that, and it more than paid for beers and thatch huts. Then one time I tried not cutting my bill rate in half. Nobody but me seemed to notice. So now I don't do that anymore.

Neither should you. The work you're doing is exactly the same regardless of where you do it from. Charge accordingly.

Not making any assumptions, just reading the OP. I was thinking more about employees than freelancers/contractors. In that case it's your business run it how you want and if your customers are willing to pay you're in luck!

Edit:spelling

No of course not.

Remote working engineers are paid for their performance on the "remote market". So you don't compete with engineers in SF but worldwide. Maybe you will have a different salary than a engineer in SF, but it doesn't matter if you live in Austin or in Auckland.