TSMC has experimented with the initiative. In some specific cases, major EDA vendors (Cadence, Synopsys) host the PDK on their cloud platforms. You can click "Download" only after you sign an NDLA (Non-Disclosure License Agreement) via a click-through portal on the vendor's website. This is as close to "public" as it gets, but it still requires legal paperwork.
An interoperable format that works across different tool suites. Virtuoso/Custom Compiler PDKs: Specifically tuned for Cadence or Synopsys environments. The "Open" Alternative tsmc 65nm pdk download