Should the left favor strong, central government? They often seem to do so as a matter of principal. I think this is a mistake. Many important fights get won at the local level. They establish a foothold in a few localities and then spread to the rest of the country. The ultra-stagnant, conservative federal government simply does not move fast enough.
Gay marriage, for example, appeared to get a foothold when the mayor of San Francisco, Gavin Newsom, directed his city clerk to issue marriage licenses to gay couples. This eventually was adjudicated in California's state supreme court, which legalized gay marriage in the state. I don't know if the 2015 supreme court decision legalizing gay marriage countrywide could have happened without this initial kick at the local level.
Marijuana legalization also got its start at the state level. California legalized medical marijuana in 1996, with extremely lax standards on who can get a prescription. This was de facto legalization for the nation's largest state. I doubt if the states currently legalizing cannabis would have been so emboldened without California's example. And I doubt if public opinion would have changed so quickly without this kind of policy "experiment" at the state level. There are now several states that have adopted full legalization (well, regulated legalization, at any rate). We can point to them and say, "Look, nothing terrible happens after legalization." There isn't an explosion in vehicle accident rates, or even in cannabis use rates. You don't see really see any change in the trend line of social indicators. (Well, there's the obvious one: fewer arrests for nonsensical nonviolent "offenses".)
See no-fault divorce as another example of something starting at the state level. Once again, this is California leading the pack (under governor guess-who). I don't know the history of decriminalization of homosexuality (remember, there used to be police resources dedicated to prosecuting gays!), but from what little I know this started at the state level. The Supreme Court finally forced a recalcitrant Texas and 13 other states to fall in line in 2003, when it struck down state anti-sodomy laws as unconstitutional. But we probably never would have gotten to "Federal government puts a few hold-out states in line" if we hadn't first had "A few extremely progressive states relax their sodomy laws, against the grain of national popular opinion."
Sure, there are cases where a state or local government is "misbehaving" and needs to be told to straighten up. There were certainly some southern states that held onto racist laws for way too long, and it's probably a good thing that the federal government made them change their racist laws. But once you've so empowered the federal government, you've created the danger that it will start doing the wrong thing in every state. I don't see any particular reason to think the federal government gets policy right more often than it gets it wrong. If the federal government is weak (and can't "fix" bad local policies), then, sure, some states will have bad policy. But people can move away from those states. This weak-but-still-important mechanism of error-correction is missing at the federal level. Migrating to another country is far more costly (traumatic even) than leaving a messed-up state. I don't think it's appropriate to trot out the example of southern states in the era between the Civil War and the civil rights movement as a "proof" of the need for strong federal intervention. It is very hard to argue that this example generalizes. How about the Soviet Union? Did it "fix" the "mistaken" policy of its subject states? Is it a good thing that China is controlled by a central government? How about India?
Don't mistake me as arguing that local sovereignty is inherently more conducive to freedom than a strong central government. The worst states can be just as stifling of freedom as the central government. Even at the very local level of cities or counties, the police force can become a government unto itself and often operates as an extralegal policy-maker. But with empowered local governments there is more experimentation, and more chances to avoid the worst abuses of government by moving away from the truly bad ones.
I get annoyed when I see various slogans and memes on Facebook, decrying that a politician at the federal level has ceded some power back to the states. This is always done far too glibly, as if there weren't a trade-off between having stronger states versus a stronger central government. As if the central government were error-free and the state governments were always at fault. My cynical interpretation is that people really aren't very principled, but just want this particular culture war conflict adjudicated in their favor (whatever happens to be the outrage of the week). Sometimes that means embracing states rights, and sometimes that means embracing a dominant federal government. Which one a person embraces often depends very much on who is "winning" that particular battle in the culture war. If, say, gay marriage doesn't have a foot-hold yet, its supporters tend to embrace states rights. If gay marriage is well-established in many but not all states, those same supporters tend to embrace a strong federal government "forcing" the last few hold-outs to step in line. To me, it all looks like cynical posturing and strategic outrage, calculated to win policy concessions. I wish that the people making these kinds of statements would articulate a principle and stick by it even when it's not convenient. That's the thing about principles: they still apply even when we wish they wouldn't.
Edit: I begin this post by addressing the left, but I should note that conservatives can also be seething hypocrites when it comes to "states' rights." It seems that they (some of them anyway) want a federal drug war to squash local experiments in cannabis legalization. And it seems they (again, some of them) want federal intervention to prevent cities from being sanctuaries for immigrants.
I avoided the term "federalism." Many people think it means "the supremacy of the federal government" while it actually means something more like "states' rights." People who argue that a policy question should be left to the states are arguing for federalism. Of course "state's rights" carries some historical baggage, but "federalism" is potentially confusing.