Can States Preserve Voter ID?

HR1 supposedly ends voter ID, through Congressional authority under Art. I, sec. 4 to regulate elections to the House and Senate.  They can prohibit States from requiring voter ID for federal races.  But there are few federal elections that are not also State or local elections as well.  Require voter ID for those elections and assess a hefty fine for using a fake ID.  The 24th Amendment prohibited the use of poll taxes to prevent voting in federal elections; because these were so heavily tied to local elections in the South, it pretty well ended poll tax disqualification for State and local elections.   It can work that way here.  I do not see a way for Congress to require States to hold federal elections on different days from State elections.