There is a discontinuity in curvature where each arc meets. It’s possible to make joins between curves smoother using Euler spirals, but I don’t know how to use them well enough to apply them to eggs. https://en.m.wikipedia.org/wiki/Euler_spiral

I recently tried to draw f holes using Euler spirals, but they turned out too short and fat, and I gave up on them. But they are quite fun to draw on a computer by simple numerical integration, ignoring all the more complicated mathematics in the wikipedia article. Perhaps I could have made my f holes more elegant by understanding the parts I ignored… https://en.m.wikipedia.org/wiki/Sound_hole

The issue is more the smoothness in the change in curvy-ness:

https://www.figma.com/blog/desperately-seeking-squircles/

If you sit in a rolling car and the driver suddenly presses the break vs eases it in, you could halt with the same deceleration and yet one will feel smoother than the other.

The car's position is not discontinuous, the velocity isn't either (in both cases it has to slow through intermediate velocities).

It is the decelaration that in one case grows suddenly and in the other changes smoothly.

On an egg, there is no place where curvature changes suddenly, and yet on a four point egg there are points where it does exactly that.