The EPA was created by Nixon to simplify and streamline the Executive Branch agencies enforcing the following laws, all passed by a Congress and signed by a President:
Air
1955: Air Pollution Control Act PL 84-159
1963: Clean Air Act PL 88-206
1965: Motor Vehicle Air Pollution Control Act PL 89-272
1966: Clean Air Act Amendments PL 89-675
1967: Air Quality Act PL 90-148
1970: Clean Air Act Extension PL 91-604
Water
1948: Water Pollution Control Act PL 80-845
1965: Water Quality Act PL 89-234
1966: Clean Waters Restoration Act PL 89-753
1970: Water Quality Improvement Act PL 91-224
1972: Federal Water Pollution Control Amendments of 1972 PL 92-500
Land
1964: Wilderness Act PL 88-577
1968: Wild and Scenic Rivers Act PL 90-542
1970: Wilderness Act PL 91-504
Endangered species
1946: Fish and Wildlife Coordination Act PL 79-732
1966: Endangered Species Preservation Act PL 89-669
1969: Endangered Species Conservation Act PL 91-135
1972: Marine Mammal Protection Act PL 92-522
1973: Endangered Species Act PL 93-205
Hazardous waste
1965: Solid Waste Disposal Act PL 89-272
1970: Resource Recovery Act PL 91-512
Other
1947: Federal Insecticide, Fungicide, and Rodenticide Act PL 80-104
1969: National Environmental Policy Act PL 91-190
1972: Federal Environmental Pesticide Control Act PL 92-516
If the EPA were dissolved by Executive order tomorrow, all these laws would still be on the books, any President would have to take care that they be faithfully executed, and they would require separate, mini-EPAs at Interior, Agriculture, Commerce, Labor, HUD, HHS and possibly Justice.
The problem is not the EPA. The problem is Congress.
The Worst Problems with the EPA are due to the Totally Rogue expansion of authority by administrative means. NOT by Congress.