Well you already pointed at why: because you can be ordered into mental health care. You can't be ordered into confession, it's completely voluntary. Furthermore, priests do not have a legal duty of care; they are not registered professionals with professional standards to follow. Their role is defined by the church, not law and regulation.
In a practical sense, such a law isn't going to work much anyway. It would be almost impossible to prove that a priest had been confessed to, short of someone admitting it directly. So the only way it works is if the child abuser wants to get one over on their priest - giving the child abuser another avenue to hurt someone else.
It almost certainly varies between jurisdictions. However, a few minutes ago I looked it up the proposed law in Washington[^1] for this story, and it does actually require reporting of all past cases of child abuse for all groups listed (therapists and other professionals, and now priests also).
To be clear, it's the time that varies, almost everywhere has laws requiring some level of mandatory reporting. But, for example, the federal definition[^2] does not require reporting of child abuse cases in the distant past (my emphasis):
The key part is that it only covers recent harm and imminent risk. This is the baseline that's pretty much universal, but it seems many, or at least some, states have laws that go further and require all reporting. The Washington state law[^1] is summarised as:
[1]: https://app.leg.wa.gov/billsummary/?BillNumber=5375&Year=2025 - direct pdf link: https://lawfilesext.leg.wa.gov/biennium/2025-26/Pdf/Bills/Session%20Laws/Senate/5375.SL.pdf?q=20250510110254 (see Sec. 2. page 6) [2]: https://govfacts.org/federal/hhs/reporting-suspected-child-abuse-or-neglect-a-guide-for-action/