"Squircle" is a bit of a misnomer, isn't it? A "classic" rectangle with rounded corners is a rectangle with circle segments added at its corners, while a squircle actually has nothing to do with a circle. It reminds me more of the way curves in railways are designed: one might think that these are circle segments too, but that would mean that when going from the straight track to the curve, the centripetal (and centrifugal) acceleration would go from 0 to max instantly, which would lead to a sudden jolt, increased track wear etc. Instead, transition curves (
https://en.wikipedia.org/wiki/Track_transition_curve) are used to gradually increase the lateral force.