First of all does the church have the funds to be employing "Supervisors"?
Usually the person being supervised pays for it. It is a tax-deductible work expense, though.
Parish priests already have a formal supervisor in their bishop or archbishop.
No, that's a different relationship. We're not talking here about operational supervision. And remember that this requirement is intended to address some of the issues that arose when bishops or archbishops were not providing adequate oversight.
They have other priests or pastors they can talk to.
This is true, but coffee with a friend isn't the same, either.
It sounds more to me like someone that a priest or pastor can go to if they have issues that are bothering them, and in the case of Catholic priests at least, the confessional is out of bounds in the sense they can't mention the emotional load someone else's confesssion might have on them.
You can, in the sense that you can say, "I heard a confession, and it had this impact/brought up these issues for me." You don't need to talk about the content of the confession.
Unless the church is going to employ outsiders to fill the role, possibly a formal or informal network of religious (or church employees) who can be relied up to support each other might be a better way to go.
There's no real quality control with that, though. Formal supervisors have to undergo training, they maintain accreditation, and they have clearly spelled out boundaries and ethical frameworks. A network of peers or the like would be much more hit-and-miss as to what is possible.
I don't think the "sheep" should be doing the supervising.
I agree that your supervisor should not be someone under your pastoral care. It's not just that they judge (although that's true too), but that it helps to have someone with a bit of distance from the dynamics of the day-to-day issues and personalities you're dealing with.
