So why doesn't the President push for a constitutional ammendment banning abortion?
Because he knows it would not get 3/4 of the states to agree to it. He also knows that the abortion question will be returned to the states when he appoints the next two Supreme Court justices and Roe v. Wade is overturned.
And as I pointed out earlier, the President has no authority over a constitutional amendment. He is entirely out of the loop. If it is passed by 2/3 of Congress, and 3/4 of the states it becomes an amendment -- the President does not have to sign it or do anything.