Also, the borders aren't arbitrary: there are governmental structures that have built up and settled over centuries.
Really, I think there's no reason most of the laws we argue about should even be done at the federal level. We just do because the media is national, so it seems convenient and it makes for a more firey discussion, and we forget that we don't even need to agree with the other side. We can each do what we want.
Let me turn the question around and ask why you're so determined to tell people in another state what to do?
To try to answer your question. I think there are common rules that make sense to apply globally (eg no murder, slavery, theft of private property, etc...), and some rules that should be very local (eg maximum sizes for billboards), and there's some middle ground for things like regulation and management of watersheds.
IMO this isn't true now, and it's demonstrably been getting less and less true in recent years[1]. The claim that states seem like they have different cultures if you consider it isn't really helpful either: The human brain loves imposing structure on things, so if you claim that a certain area is a single entity, naturally one's tendency is to think of things as "Californian" or "Arizonan", etc. In much the same way, one thinks of an Italian living on the French border as ethnically Italian, and a guy living a few miles away as ethnically French. Drawing arbitrary lines is convenient enough, but pretending there's any sound reason behind these distinctions is silly (look at the recent history of Central/Eastern Europe to see exactly how arbitrary state lines are).
[1] I'm referring specifically to the fact that it's a well-studied phenomenon that the urban/suburban/rural divide in culture+values is becoming a lot more significant than the state-to-state ones.