The screwed-into-a-tabletop ones we used to have at school in the 80’s and 90’s were great, with the crank and rotating blades. Was easy to make razor-sharp pencil points.
At home, with my kids, we only have those common cheapo sharpeners with a single angled razor blade. They sort-of work, poorly.
With those it’s too easy for the pencil point to break off, often the planed curl of wood will snap at the boundary between the two wooden halves of the pencil. It’s not smooth, and very hard to get a nice sharp point with them.
Good pencils help too. I tend to prefer German and Japanese brands like Staedtler, Stabilo, Mitsu-Bishi, and Tombow.
Then get one of those?
X-ACTO KS Manual Pencil Sharpener: https://www.amazon.com/dp/B00006IEDY/ref=cm_sw_r_cp_apa_zPGw...
$7.91.
As I posted elsewhere in the thread, author of the NYTimes article is the sometimes comedy partner of the artisanal pencil sharpener, who also wrote the definitive book on the subject.
I adore mine. It lives in a pretty cut crystal candy bowl in a nest of colored pencil shavings.