The federal government has the authority to appoint federal assessors to local property tax districts, to generate valuations for a national property taxation, and then share these updated valuations with state and local governments, which may then independently decide to use the same valuations for purposes of state and local taxation. It did so in order to collect the 1798 national property tax under John Adams and the three 1813-1816 national property taxes under James Madison.
The federal government also has the ability to regulate state and local taxes using the interstate commerce clause. After the provision in the Articles of Confederation limiting the federal government to collecting direct taxes in proportion to state land values was abandoned, the supporters of direct taxation influenced by the French Physiocrats lobbied for the interstate commerce clause in order to ban state and local governments from collecting excise and sales taxes on goods sold across state lines, so that state and local governments would be forced to rely more heavily on property tax.
I am neither an expert nor familiar with US constitutional law, but in most other countries the federal power trumps the power of any states/provinces and is not limited by a single clause and helps simplify and remove any disparities in taxation policy. As far as property taxes are concerned, most countries retain the policy to keep the local councils empowered to decide tax rates albeit "within the rate limits and fairness criteria imposed by the states and federal governments". In my country property taxes cannot be made zero/low or made exceptionally high by a showoff city council trying to get reelected for whatever reason as this causes unnecessary migration between cities/towns for no practical reason other than to skirt taxes with no practical systemic benefit to the populace at whole.
In the U.S. politicians were more concerned with the opposite, that low property taxes would be more likely to cause loss of population and emigration than high property taxes. At the time of the revolution the U.S. colonies were relying on revenue from land tax, property tax, property income tax, and public banking rather than sales tax and were rapidly growing in population due to immigration from European countries where most of the large landholders were exempt from property taxes. Early America had large quantities of land and few workers relative to Europe. In order to industrialize Franklin and founders associated with Democratic-Republican party thought it was first necessary to increase population and maximize rural agricultural productivity, which from reading the French economists they thought would be stimulated by some form of direct tax and hindered by indirect tax.
The federal government also has the ability to regulate state and local taxes using the interstate commerce clause. After the provision in the Articles of Confederation limiting the federal government to collecting direct taxes in proportion to state land values was abandoned, the supporters of direct taxation influenced by the French Physiocrats lobbied for the interstate commerce clause in order to ban state and local governments from collecting excise and sales taxes on goods sold across state lines, so that state and local governments would be forced to rely more heavily on property tax.