Yes. Cost of living should have nothing to do with it. Do we pay people with kids more because their CoL is higher? Payment should be based 100% on work.
If someone else appears equally capable and willing to work for half or a quarter of what you are, it doesn’t matter much what the work is worth, they’re going to get the job much more often than you will.
Employees want to get the most attractive compensation they can from an employer. Employers are not that different in this regard, in the other direction.
In a sense we do because they (sometimes but increasingly) get paid leave and also drive up health insurance costs. As far as health insurance goes it never seemed fair to me that spouses and children get their health care subsidized by the employer.