The smartest Ph.D students are the ones with the most potential.
This is often not the case.
Many other characteristics are crucial, and highly intelligent students may underestimate them. Being super smart but emotionally unstable or immature will likely not take you far. On top of that, there are many factors you have no control over. Your subfield may hire more people than other subfields. So you may end up getting a tenure-track job before your colleagues.
The best Ph.D students are those who were the best undergrads. Different worlds, so the correlation is not that high. Being able to test well is usually not that important in grad school. What counts in a Ph.D is having original and relevant research ideas. You can turn into real and high-quality output in the form of publications.
I agree that “A Ph.D will make you smart” is kind of a myth. Since people admitted to competitive Ph.D programs are usually (hopefully) already smart enough to be there. I do feel that a good Ph.D program can certainly help students maximize their academic potential in an ideal scenario. Obviously, you will learn a lot (including about yourself, and how you deal with frustration and failure). Even if you consider yourself dumber than the average Ph.D student, you will likely leave the program less dumb and intellectually more mature.