If anything, a PhD program teaches you how to write faster while maintaining an acceptable quality: Journal papers, conference presentations, and funding agency reports are all long-form writing projects that come up quite frequently and distract from the research (the fun part). Most of the value from this writing comes from it being accepted; improving quality beyond this level has rapidly diminshing returns.

My writing definitely improved tenfold.

That tracks. I’d add that Ph.D. laureates tends to be people who like to pursue knowledge in depth. I think it’s this, combined with the work ethic and discipline, that make them excel in certain fields.

"Hard working" and "smart" are very different things.

One could almost say that not being smart requires you to be harder working. (At least that's what I'm telling myself to keep working hard.)