I really don't find it convincing. If you pay as much as your competitors, why would talents in expensive areas would be discouraged to apply to your company and go to your competitors?

If you're assuming that big city people would feel bad because the small city people get paid more in terms of cost of living, then I'd say that's a bad assumption. People living in any city should know its pros and cons, why is it up to you to decide that the cost of living is the metric?