Did the Democrats hold primaries in 2012 so that other Democrats could challenge the President?
Of course they did. But Republicans are not Democrats and can't be held to that standard. They can choose their candidate in what ever way they want.
Did they? According to this CNN article, in at least South Carolina, they did not.
Republican 2020 primary: State parties move to nix contests in show of support for Trump - CNNPolitics
From that article:
"In South Carolina, a key early primary state, Republicans decided to nix their presidential primaries in 1984 and 2004, when Ronald Reagan and George W. Bush were up for their second terms; while state Democrats skipped their contests in 1996 and 2012, with Bill Clinton and Barack Obama running for reelection, respectively."