Why are aircraft such as the legacy F-14 and now the F/A-18 used by the US Navy carriers?

It seems to me that developing a new aircraft from the ground up is very expensive. Is it not possible to have converted F-16 or F-15's for carrier operations? Obvious modifications such as folding wings, stronger undercarriage, hook, etc. I'm sure there are many more I'm not aware of.

Is the reason that these aircraft (F-16, F-15) are not suitable for carrier operations, even with modifications?

Isn't this what the Russian Navy did with their fighters? The carrier versions of the MiG-29 and Su-27?

What are the reasons the US employs unique carrier aircraft? Is the reason political? Technical?