Correct, but incomplete.
The laws that the EPA was created to enforce were passed by Congress and signed by various Presidents between 1955-1970. Those laws are broad in scope, grant enormous powers to the Executive Branch, and do not give the President authority to ignore them.
The EPA was a cost-saving measure, so that multiple Executive departments weren't wasting resources to enforce the same laws.
It's the laws that are the problem.
The agencies are given broad authority to make up regulations to enforce those laws. These bureaucrats need to justify their existence so they make up problems and then regulations to solve those problems, going way over the intent of the law. I don’t know, but I doubt if everyone that voted for the clean air and water acts thought it would turn into a war on global warming and a person not being able to build a fish pond on his own property.