Depends what profession you end up pursuing. If your son pursues computer science then likely never need to use handwriting ever again. As a 10+ year software engineer I've never needed to handwrite anything professionally, not once. Personally, still like to do the occasional handwritten card or letter for friends and family.
Also turns out to be a different skill. (My old school printing is fine, my old school cursive was pretty much gone by day one of college, chalkboards are almost always slow block-printing - so when I started using whiteboards, it was all cursive patterns that were unreadable and mostly served as a vague reminder to the audience of what I said when I was scribbling over there.)
About 5 years ago I was inspired by a friend casually doing some amazing whiteboard art at work, and ended up trying a more calligraphic approach (not fancy gothic patterns, just that kind of intent/attention.) A lot slower, but a bunch of coworkers privately requested that I keep up the new approach...
Mostly don't even use those these days--basically never in an office. Collaborative docs are more common. I mean you need basic at least somewhat legible printing but that's probably fine for a lot of things these days.
Handwriting was always my worst grade in elementary school and don't really know Palmer script any longer.
