What kurbo does is lower to quadratic Béziers[1], then the analytic solution to nearest for a quadratic Bézier is the solution to a cubic equation[2].

I'm not sure this is the best possible answer, but it's at least pretty good, and certainly better than flattening to lines.

And I'd like for people to get in the habit of checking kurbo; the intent is for it to always have the best in class algorithm.

[1]: https://docs.rs/kurbo/latest/src/kurbo/cubicbez.rs.html#647-...

[2]: https://docs.rs/kurbo/latest/src/kurbo/quadbez.rs.html#297-3...