To the degree that kind of tracking significantly matters to you, there are alternatives that scale better and are more under your control.

Personally, I doubt stripping the URL is going to meaningfully impact Google’s ability to track through Youtube. There are well paid, well funded, bonus motivated professionals who spend years throwing data science and computational expertise at the problem. They own search, the most popular browser, and handle a lot of DNS requests.

Never mind that people tend to remain logged into their Youtube accounts, their Google accounts, and operate from the same handful of IP addresses through ISP’s who are happy to monetize data.

Privacy theater is like security theater only less effective.