I agree, there's no chance of this happening.Truth be told, I would absolutely approve of Congress doing the same exact thing. And you're right, they most likely won't because both sides will not try to compromise on their positioning in any way.
Even if Congress did pass a law making abortion legal across the country, the Supreme Court could (and this Supreme Court maybe would) declare the law unconstitutional, on the ground that it violates the 10th Amendment: powers not granted to Congress under the U.S. Constitution are reserved to the States, and the people.
In 1995, the Court invoked the 10th Amendment to invalidate a federal law making it illegal to carry a firearm in a school zone. The vote was 5-4, with the 5 Republican-appointed Justices in the majority. The Court said the legislation had no meaningful connection to interstate commerce, the constitutional basis that Congress relied on to justify the law.
Our federal system of government creates a bit of a mess here. In the U.K., or pretty much any other country, if Parliament passes a law, that's the end of the story.