The Constitution does not delegate the power of regulating elections to the United States, and does not prohibit the states from doing so.
This line I quoted, art. 1 sec 4:
The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Places of chusing Senators.
-- is a bit ambiguous, sure, but it's obvious that congress can regulate the electoral process for federal representatives from the states, and they have already passed around a dozen laws doing so since the original 1840/42 apportionment act (most in subsequent apportionment acts), most recently
the 1967 law explicitly mandating single-member districts:
In each State entitled in the Ninety-first Congress or in any subsequent Congress thereafter to more than one Representative under an apportionment made pursuant to the provisions of section 2a(a) of this title, there shall be established by law a number of districts equal to the number of Representatives to which such State is so entitled, and Representatives shall be elected only from districts so established, no district to elect more than one Representative (except that a State which is entitled to more than one Representative and which has in all previous elections elected its Representatives at Large may elect its Representatives at Large to the Ninety-first Congress).
This is also really off-base:
Things like the Voting Rights Act are allowable only because they are enforcing the 14th Amendment, which it is almost impossible to argue that switching to a variant form of voting would do.
The big motivation for the 1967 act from congress requiring that state governments use single-member districts was to prevent southern governments from switching to a different voting variant in order to circumvent the Voting Rights Act and the 14th amendment. In the courts as well, the bulk of the debate around state districting at this time and to the present has centered on the use of gerrymandering for racial disenfranchisement, and whether minority-majority gerrymandering aimed at increasing minority representation was justified.
The main point of this being that congress could just as well require a different system. It would probably get struck down by the Republican-dominated supreme court, but that would be a partisan ruling exploiting the textual and historic ambiguity.