Look at it this way, can, or should, the state be able to override a county's ability to limit a cities property tax? If so then why should it be limited to the state, and why should the fed not do the same?
Well, the legal reason is that the US government is Federal, and the state governments typically are unitary.
That is, under the US constitution, the states have a limited degree of sovereignty. However, under state constitutions the local governments typically do not have any sovereignty.
That is why states can and do charter and abolish local governments as the need arises. If your school district has an abysmal educational record, your governor can appoint somebody to come in and basically run the district. They'll listen to the locally-elected school board, but ultimately they are a dictator accountable only to the state. Your only recourse is to go to the state government for relief if you don't like it. In contrast, the President of the US cannot do the same thing with a local school district. At most he can withold Federal funding, though in reality this is a pretty big stick.
That's the reason for the situation as it stands, and it has its roots in the history at the founding of the US. Before the US Constitution there were the Articles of Confederation, and under that charter the US government was even weaker - it had no real sovereignty of its own and was a bit like the UN.
This is in contrast with how most nations function. Most governments are unitary in design. The PM of the UK can in theory fire a random teacher in a random elementary school, since ultimately the whole chain of command reports up to them. In practice they usually have local councils/etc, but typically there is no true sovereignty other than in the sense that the national government imposes rules upon itself.