I don't agree. PAIP goes well beyond "introduces as much CL as necessary to carry out the task" in its Common Lisp presentation. It could easily serve as a first book for someone to learn Common Lisp, even if that person has no interest in AI whatsoever.
Some of the examples in PAIP may be outdated in a historical but not practical sense. I've joked in the past that the code is so well-written than it can be excised and framed on a wall. With code this good, the lessons one can learn are numerous and the code stands the test of time.
Unfortunately, the same can not be said about the PCL examples since - to name two - there are far better ways to do binary parsing and pathname handling today than binary-types and cl-fad. The PCL examples are a product of the time that they were written but they are tied to a particular verbose, subjective style and were not "optimal" or even particularly good, back then.
Ultimately, PCL introduces Common Lisp to the audience as does PAIP. The difference is that reading PCL in 2020 will have minimum, let's say thought-provoking, impact. Reading PAIP (or Let over Lambda, SICP, On Lisp, Lisp in Small Pieces) remains -and will remain- a paradigm-shifting experience.