I have a question as a potential remote employee: If I live in a city with a very high cost-of-living, will it be difficult to find a remote position that pays reasonably well relative to my cost-of-living?

I assume one of the biggest benefits to hiring a remote worker is you can hire someone with a very low cost-of-living and pay them relatively relative to that. But if I'm living in a place with a high cost-of-living and the company can hire someone from any part of the world, why wouldn't they wait and find someone that's super inexpensive?