The Consttution delegated a short list of powers to the Federal Frederal Government and all powers not enumerated in Article 1 Section 8 were reserved to the states, Passing laws pertaining to marriage were among the powers reserved to the states and Congress violated the Constitution when in1882 they paassed the Edmunds Anti Polygamy Act.
government was prohibited frrom The Bill of Rights asserted that individuals had the right to practice their religion passing the Edmunds Anti Polygamy Act also violated the 1st Amendment.
The only way the Federal government could lawfully ban polgamy would have been to amend the Constitution.