I think that using the paraboloid surface to correct spherical aberration only applies to mirrors, not lenses. For mirrors the correction for spherical is, of course, perfect. Off-axis perfomance is, however, not great, which is the reason that Schmidt optical designs are often used for wide angle telescopes.
Engineers often face problems where they need to optimize three parameters, such as fast, good, and inexpensive. Then they say "you can have any two of the three. Which two do you want?"
And nevertheless I often hear from managers that they want all 3. Then I reply - show me, let's work together week or two, and show me how. They never did.