Am I missing anything here? E.g. should I expect pieces of C code that handle completion in elisp mode?
Probably, yes. „org-babel“ can execute shell code inside an org document but always asks the user before it does. You can disable this if you want to. No big deal. Should totally work like this in elisp-mode, too.
Looking at elisp-completion-at-point and likely deeper into elisp--completion-local-symbols, I'd try to find where macroxpansion occurs, and make it conditional. Same for the explicit emacs-lisp-macroexpand.
I would also search for `(eval ` in general and maybe put it under a buffer-local flag, too, so that you won't press C-x C-e or C-M-x and execute malicious code by mistake, when you know you're working on a piece of malicious code.
Maybe instead of a defcustom, it should rather be a minor elisp-paranoid-mode which would do all kinds of things to prevent execution of the code in the buffer, or the code the buffer refers to, etc.