You were being downvoted here, but I think you make a great point.
The problem with having separate client-side and server-side validation logic is that you (generally) want the rules to be the same, but you end up needing to write them twice, usually in completely different technologies. I have seen many, many cases where the client-side validation and server-side validation got out of sync, and then just like you put it, obscure bugs or security exploits can arise from this.
In general, I think client-side validation should really only be used for the basics, often with respect to type (e.g. the email/URL examples given) and just basic "required" (non-empty) fields. Anything more complicated than that should be done solely server-side in my opinion - e.g. I wouldn't use setCustomValidity with a complex set of client-side rules. What I think is important, though, is to ensure that if the server validation fails that the error message that comes back is not just a single "Bad input!" message, but errors can be keyed by field to ensure you can display field-specific error messages and error highlighting.
Another option I considered back in the day when my backend was on NodeJS is to have the server return the text for a JavaScript validation function before the form itself is actually rendered. This, this function can be run client-side for immediate feedback when the user submits the form, but it's also the exact same logic that is run on the server when the form values are received.