So who should install an association president? Whoever would make the oath special for the person being installed.
There likely isn't something that "requires" someone holding a specific office to conduct a ceremonial installation - so the power to administer an oath could be whoever the association may allow (i.e., vest that power with). We've had it be past presidents (the one they want), national presidents, past national presidents, our association legal counsel, someone in their company special to them (typically company owner), another president they served with at local level, a legislator, a relative .... and even an association executive.
Nothing makes an evening quite as, um, questionably special as an installation by someone they've never met before - even if that person holds an office somewhere. Almost guarantees the name won't be pronounced correctly.
Our question to incoming president: Who would you like to install you? We want it to be special for you.