The current PKI system was designed by Netscape as part of SSL to enable secure connections to websites. It was never independent of the web. Of course PKIs and TLS have expanded beyond that.

"WebPKI" is the term used to refer to the PKI used by the web, with root stores managed by the browsers. Let's Encrypt is a WebPKI CA.

The idea of a PKI was of course designed independently, there are many very large PKIs beyond WebPKI. However the one used by browsers is what we call WebPKI and that has its own CAs and rules.

You're trying to make it sound like there has ever been some kind of an universal PKI that can be used for everything and without any issues.

> What exactly do you mean with "WebPKI"?

WebPKI is the name of a specific PKI system, where PKI us a generic term for any PKI.