IL took that function away from the SoS in the 1970 constitution.
The current State BoE has 4 Dems and 4 Pubs. IL state law also provides a mechanism for counties and cities to establish boards of election to replace that function of the elected clerk. I think that's a very reasonable solution. The electoral process should be completely fair for all sides. Anything related to elections should be decided by a nonpartisan panel, such as the Wisconsin's Government Accountability Board (and something along the lines of California's Citizens Redistricting Commission for redistricting).