Defining parts of the language as executable code instead of prose is attractive. One drawback is over specification - the reference implementation may have inessential features that a prose version could leave to the implementor - but overall I think that risk is minor compared to having executable test cases/examples embedded in the standard.

Arbitrary size integers written in lisp is a thing. Maybe gambit and sbcl? Can't remember offhand. Calling down to llvm.sum.i64 or w/e is very similar to calling down to x64.