Why isn’t showing the filter bar on product detail pages common?

Typically on ecommerce or classifieds sites (I work with auto dealers specifically) the search results page (srp) contains the filters and any applied filter state searched. Ex:

However clicking on one of the results and going into the detail page, we don't show the filter bar. The user then would get back to results by going back (button or browser nav).

This is a pretty ubiquitous ux throughout the web, from Nike to Cars.com to eBay.

A client recently requested to add the filter bar from the SRP to the details pages as they thought it would reduce effort to continue searching. While I knew this wasn't common ux, I was having trouble explaining why I was pushing back.

Instinctually, I know that it's weird to have active filters show on a detail page when the bucket of data being filtered isn't visible. I could see having a text search always available in the nav area, which is more common now. But having some trouble coming up with a concrete reasoning other than -- "no one does that".

I would really appreciate if anyone could give some insight on this common ux standard or point to any known research on this topic (I couldn't find myself when searching the topic).