Two classic tales on this subject.
First, Joe Garagiola used to talk about how Ted Williams spoke of hitting a curve ball by picking up the spin on the ball. JG found that unhelpful, as he found it hard to see spin when the ball was already coming at him at 90+ mph. Late in his career, Williams' eyesight was tested and found to be 20/8. JG quipped, "No wonder HE would say that. He could see the spin. Heck, he could read Happy Chandler's signature."
Second: Wade Boggs had excellent natural eyesight as well. One year in spring training, a bad hop during infield struck him on the forehead and left him with some blurring and, even when that cleared up, a diminution in his acuity. He hit under .300 that year for the first time in his career. During the off season, he got contacts for the first time and worked a lot on acuity exercises. His average was restored to well over .300 (though he did taper off as he aged).
I have long advocated having players ask their optometrists to correct them to 20/15, not the standard 20/20. In reality, your son might be 20/40 and your optometrist might not see a big need to wear lenses, or your son may find the correction more trouble than it's worth. Well, he can go without everywhere else, but he should pop those contacts in before he steps in the box. I guarantee you will notice a difference in performance.
I don't know if baseball improves your eyesight, but it's a reality that keen eyesight is critical to peak performance in baseball. So perhaps it's self-selecting in that way. Those with lesser vision wash out.