Lets see if I got this right:
State cultural differences allow the different states to mandate different abortion restrictions? Nope.
State differences allow some states to enforce Jim Crow Laws? Nope
State differences allow some states to impose additional restrictions on self-incrimination? Nope
State differences allow sone states to prohibit carrying arms? You bet!
Pass the law, have New York or California or whoever take it to the Supreme Court, and see what they say on the matter.