Primaries and caucuses in the US can get cancelled and some did get cancelled, e.g.:
The shutdowns aren’t without precedent. Some of the states forgoing Republican nomination contests have done so during the reelection bids of previous presidents. Arizona, GOP officials there recalled, did not hold a Democratic presidential primary in 2012, when Barack Obama was seeking a second term, or in 1996, when Bill Clinton was running for reelection. Kansas did not have a Democratic primary in 1996, and Republican officials in the state pointed out that they have long chosen to forgo primaries during a sitting incumbent’s reelection year.
South Carolina GOP Chairman Drew McKissick noted that his state decided not to hold Republican presidential primaries in 1984, when Ronald Reagan was running for reelection, or in 2004, when George W. Bush was seeking a second term. South Carolina, he added, also skipped its 1996 and 2012 Democratic contests.
As you might guess, the likelihood of a primary/caucus being cancelled seems highest for the incumbent president's party.
But it's unclear from that article what was the election with the highest number of cancelled primaries/caucuses. So... which one was it?
(For the sake of this question being meaningful, we should probably only consider elections since 1900 or, when primaries/caucuses became widespread.)
Let's [also] consider years other than 2020, because the ongoing Covid-19 crisis would probably easily top the charts in terms of events cancelled. (I wrote this q before there was a lockdown in the US.)