Should courts be allowed to have “local” rules of procedure or should all courts?
whether they are local, state, or federal follow the same set of procedures. Why?
The Courts are independent bodies of the government. They are allowed, and required to establish a set of rules for the proper administration of their tasks.
Local government have the same independence...
Think of it this method, the main sticking point of the Constitutional Congress was the issue of small state versus big state structures. One did not want the other to dominate the nation, or federal policy, therefore the founding father built in the independence, and limited the powers of the federal affairs of state, instead of imposing national structures which you propose.