SBCL does not create binaries per se, but dumps the program image. While it practically is a binary, it's not equal to an executable that a conventional compiler/linker produces.
That distinction isn't important here, though. It is the reason the resulting file is so big, but for all practical purposes it's a binary that statically links the full CL runtime.
Because no one wrote one. There were some attempts but nothing which would work now. Delivering small applications does not seem to be a focus of SBCL users.
Commercial Lisp implementations like LispWorks and Allegro CL have a treeshaker for delivery, but that's not too surprising, since these products are for developers of applications and the users pay for such features.
In lisp eval does not take a string as its input, but a form, i.e. a linked list, containing the program to execute. Maybe you confuse it with JavaScript or Python eval (or the like) where the function both reads in a string and runs the program it parsed from that string. There are diverse functions to convert a string to a symbol in different lisps.
i think the symbol plus gets evaluated to #<function+> and then is called with 1 2 3 - CL will do apply, of course, not sure about scheme and funcall. I'm totally willing to accept my mental model is wrong, i don't have an interpreter handy.
you could, of course, look for the handful of ways to bind symbols to functions, maybe do constant folding and include a minimal set if the compiler can prove what's actually needed.
but in general i think tree shaking is hard when you can load things like that dynamically.
(funcall #'+ ...) does not do a symbol lookup and does not need to retrieve the function from a symbol in Common Lisp. (funcall '+ ...) would retrieve the function from the symbol.
Treeshakers are generally used for application delivery in Lisp. When you do that, then one usually limits the amount of use of runtime dynamics. Typically you can tell the treeshaker what to remove or what to keep: the compiler, the symbol table, debugging info, etc etc.
Allegro CL and LispWorks have extensive facilities for this.
More briefly, in a half decent implementation, the + symbol is involved in the processing of (funcall #'+ ...) in the same ways and at the same times as it is involved in the plain call (+ ...).