One of the ideas that the study of state constitutions makes particularly easy to understand is the slipperiness of categorical boxes that we often take for granted. On the surface, for example, it's easy to put explicit separation-of-powers clauses (which many state constitutions have, modern administrative state to the contrary) in the structure-of-government box, while free-expression clauses seem to fit neatly in the individual-rights' box.
But in practice, some of the most important rights in the daily lives of Americans are decided by structural clauses (which, I know, we also see at the federal level). For example, whether pensioners in Pontiac, MI will continue to get the health benefits they bargained for turns largely on the obscure structural question of whether the state legislature complied with a constitutional clause that requires a 2/3 vote to give effect to statutes sooner than 90 days after the end of the legislative session (you'll hear more about this at Wayne Law Review's exciting symposium on Oct. 11).
Even within the structural category, vertical and horizontal allocations of power can seem clear but become fuzzy upon closer inspection. In most states, constitutional clauses providing for local governments offer a version of autonomy that permits them to carry out a broad range of government functions unless otherwise prohibited by law (home rule). Superficially, these clauses are about the relationship between the state and its localities. Just as significantly, though, except in the few states where home rule provisions are so strong that local ordinances can trump overreaching state statutes, home rule clauses that authorize local autonomy "subject to law" can also be understood as separation-of-powers clauses. Historically, courts used to examine municipal exercises of authority, in common-law fashion, to determine whether they were "really" local functions. Home-rule type clauses tell the courts not to interfere when a municipality regulates private parties. But these clauses still typically permit the legislature to interfere whenever it wants; the statute always trumps the ordinance. So home rule takes power away from the judiciary and leaves it with the legislature.
I think that structure-of-government issues can strike students as excessively abstract or theoretical. The fuzziness of the category distinctions that state constitutionalism highlights makes it easier to convince students that there is intense practical value in being able to argue constitutional structure on behalf of clients big and small. Advocates who fail to consider state constitutional structural questions when fighting for or against state regulation of any sort are just leaving money on the table.