I think you're conflating Common Lisp and CLOS. CLOS (usually implemented using the MOP but not required) is a facility provided by Common Lisp, but there's no requirement that Common Lisp itself be written in such a way that it actually use CLOS where possible. As Rainer mentioned, the Smalltalk VM isn't purely written in Smalltalk and Common Lisp is (often) already largely written in Common Lisp (there is some low-level support code in assembly/C/whatever and some native libraries utilized to provide the Lisp runtime environment just as there is for the Smalltalk VM. I would suspect that there is more of it for the Smalltalk VM due to the higher-level abstraction that the VM provides and more support/glue code needed to maintain the facade.)
What I think you're actually getting at is if it would be useful if more of Lisp itself were written in CLOS (which at that point would probably not be Common Lisp anymore) since Common Lisp as it is usually implemented does not generally use CLOS (at all?), but rather makes CLOS available as an optional OO framework for your applications. As it is (commonly) implemented, Smalltalk is focused on messages being sent to methods (i.e. making decisions at runtime) and Common Lisp is more focused on macros calling (non-generic) functions (i.e. making many, but not all, decisions at compile-time.) These are fundamental design and implementation decisions but there's no reason you couldn't create a Lisp that had a more Smalltalky 'feel' by utilizing CLOS and deferring more decisions to runtime.
As you've already noted, Lisp already has a very dynamic environment with a similar interactive 'feel' to Smalltalk, so what would this get you? Generally, you'd get the more extreme dynamism that the Smalltalk runtime offers and from a code organization standpoint you would replace a lot of what alist, plist, defparameter, defvar, and to an extent what namespaces are used for with object slots. You would probably also end up with a smaller set of more general functionality (Common Lisp offers a kitchen sink approach to functionality: macros and functions for nearly every use case you can imagine) to support the more extreme capabilities that OO can offer (i.e. transparent proxy objects become trivial to implement, overriding subsystems like the debugger becomes easy etc.) While there are still differences in OO implementations between Smalltalk and Lisp (single vs. multiple-dispatch, single vs. multiple-inheritance, methods vs. generic functions, message sends vs. function calls etc.), I think this could probably get you 95%+ of what Smalltalk offers. What does it cost you? Compile-time clarity and runtime performance... a price Smalltalk pays currently. Probably of greater concern to most Lispers would be that code would look and feel different from what they're used to not unlike how Clojure is different from Common Lisp. So what you'd end up with is a new Lisp with a Smalltalky feel rather than another Common Lisp implementation.