Now none of this prevents you from extending lisp in such a way that lets you freeze the method dispatch (see e.g. https://github.com/alex-gutev/static-dispatch), but "a modern compiler will jmp past the type checks" is false for all of the CLOS implementations I'm familiar with.
1: SICL is a research implementation that has first-class global environments. If you save the global-environment of a method invocation, you can re-compile the invocation whenever a method is defined (or removed) and get static-dispatch. There's a paper somewhere (probably on metamodular?) that discusses this possibility.
To clarify, as you know CLOS isn’t the CL type system. I was particularly thinking about things like fixnum arithmetic.
The CMUCL and SBCL manual sections on code generation discuss this and it can be verified with DISASSEMBLE.