Common Lisp had a lot thought put into it, but the design goals were different. One of the design goals was to support efficient compilation given various constraining dimensions: the need for speedy compilers vs. the need for delivery of applications on standard hardware. Thus a Lisp compiler should be able to generate fast code, even by using whole-program compilation. Thus the language has to take care of a wide range of possible implementations, not just one on a particular virtual machine.
Clojure OTOH has a relatively straight-forward compiler written in Java, only targetting the JVM in a standard way. The Java/JVM infrastructure for code generation (JIT), low-level optimizations (JIT), memory management, application building and delivery could be reused. With all its features and limitations (for example no TCO, fixed JVM instruction set, ...).
Common Lisp also not only provides some generic operators, but also lots of non-generic operators. One reason for that is the will for backwards compatibility (which was another goal in the Common Lisp design) and the idea that something like Common Lisp is also a low-level languages or provides at least a layer of low-level stuff, functions you would use to implement higher-level stuff.
Common Lisp is the next step in the evolution of Lisp I to Lisp 1.5 to Maclisp to Zetalisp. Thus it contains much of the core Lisp functions, stuff you can read about it the Lisp manuals from 1958 and 1960. People did not want to throw their code away, they wanted a modernized Maclisp. Thus one could port a 100kloc Lisp program from Maclisp or Zetalisp to Common Lisp without too much effort. The main operations were there.
Clojure OTOH has almost no backwards compatibility to earlier Lisp dialects. Programs can not be ported from Lisp to Clojure in a useful way. They have to be rewritten. But that was okay, since the main target were not Lisp developers, but people who wanted a language with Lisp influence in the Java/JVM eco-system (or possibly other eco-systems too).
Thus Common Lisp looks to you like it has less thought put in, where people actually struggled to be backwards compatible and modernize the language at the same time.
So Common Lisp has lots of non-generic functions, a layer of generic non-extensible functions (like the sequence layer) and a mechanism for extensible generic functions (CLOS). Something like CLOS is implemented on-top of the non-generic Lisp, with a few parts using implementation specific mechanims. One does not need to use the primitives of a different host language, because Common Lisp is already capable of hosting with its primitives.