While true, you're going to miss out on some percentage of applicants that are willing to interview a bit more to get a non-adjusted rate. This might be fine if you have a good hiring funnel, but if you're a scrappy startup, this could be challenging.

Also, you will likely end up with a slightly higher churn rate (since smart employees will continue interviewing to see if they can get a higher salary from a place that doesn't adjust based on cost of living).

It's a perfectly reasonable approach to take as an employer, and if you can make it work, all the more power to you.