In 2022, removing a few megabytes of data doesn't seem worth the maintenance cost of the feature. In other words, for most users, it's a non-problem.
And assuming he doesn't want what he wants is kind of in bad taste. You don't know his requirements.
Yes, and what exactly constitutes "dead code"? Tree shakers rely on heuristics that can fail in practice. There is provably no way to remove functions from a Lisp image and guarantee your application to work. LispWorks has a "tree shaker", but has umpteen options to tame it so your application doesn't inadvertently break.
Fortunately, it is possible to remove these functions if you, an application developer, so please. Nothing stops you. It's not even difficult. But SBCL has not implemented these (potentially fallible) heuristics for you, because (and only because) an insignificant number of users would find shaving a little binary size off to be valuable at the expense of program correctness.
The kernel supports manual tree shaking: "make menuconfig" and prune away.
Neither did sbcl support cross compiling. To the best of my knowledge all you can do with sbcl is save an image.
When I was looking in to this I read through many discussions where the developers appeared hostile to the idea of implementing these features. A common refrain I encountered was that tree shaking is unnecessary because the core images are compressed.