Because that's harder to write the laws for

Not if you assume people could understand basic math, such ... oh, any continuously valued polynomial ....

I hear this explanation a lot but I think it's a convenient fiction. Lawmakers, at least in the US, don't seem to write their own legal texts very often. Sometimes they don't even read them [1]! Congress has no problem producing monstrously complicated laws, in any case.

I think it's likely that politicians and their funding sources have found ways to profit off of these discontinuities. The infamous Medicare "donut hole" [2] was arguably a "benefit discontinuity" of the sort mentioned by the author and pharmaceutical companies profited off of it (more than a hypothetical Medicare structure without a donut hole, not relative to the spending cap that replaced it—which profits them even more).

[1] https://www.pennstatelawreview.org/penn-statim/dont-be-silly... (2013) ...which argues that this is a good thing!

[2] https://www.medicalnewstoday.com/articles/what-is-the-medica...