Should transparent HTTP proxy remove hop HTTP headers?

I read that HTTP proxy should be removing hop HTTP headers (https://www.freesoft.org/CIE/RFC/2068/143.htm)

It makes sense since some of these headers are connection-related.

The question is. Is this RFC applicable for explicit proxy only or should be it be done on transparent HTTP proxies too?

Just to give you an example. Let say a client does HTTP call and it has an explicit proxy set. However, there is a transparent proxy in the middle. So, the overall pipeline looks like that

Client ↔ Transparent Proxy ↔ Explicit proxy ↔ Web page

An explicit proxy may require authentication and will send back Proxy-Authenticate header.

If a transparent proxy removes this header (per RFC) then the client won't be prompted to authenticate and nothing will work.

This one jumped out immediately, but I think some other scenarios could be envisioned when it looks like transparent proxy should NOT be touching hop-by-hop headers.

Am I missing something or hop-by-hop removal rules are applicable to explicit proxies only?