From a lens designer perspective:
Any lens design has a large number of compromises (between center and edge resolution, vignetting, weight, size, cost etc.). As a result, lens designs are targeted at specific sensor sizes, and may not be optimal for other sensor sizes.
What exactly may not be optimal if say using a FF designed lens on a crop sensor?
- Pixel center resolution may be lower (as crop cameras usually have higher pixel density), and/or
- FF frame lenses are big and heavy to keep vignetting under control, on FF. This is usually an overkill for crop cameras: you could shave off a lot of glass and get a much lighter (and perhaps cheaper) lens, but still get an acceptable vignetting, and/or
- More glass in FF lenses may also mean slower AF (as the moveable lens elements have more inertia),
- So a crop camera user may end up paying more for a heavier FF lens with a comparable, or even lower quality, compared to a good crop lens.
Please note my using italics to emphasize a typical situation. For some FF lenses this may not be true.