Constitutionally, elections are governed by the states. He can't just stop elections. The federal executive literally has zero power over them, and that is by design.

The country's election system is highly decentralized. While the U.S. Constitution does set parameters for the election of federal officials, state law, not federal, regulates most aspects of elections in the U.S., including primary elections, the eligibility of voters (beyond the basic constitutional definition), the method of choosing presidential electors, as well as the running of state and local elections. All elections—federal, state, and local—are administered by the individual states, with many aspects of the system's operations delegated to the county or local level.

But what he could do, and what I think he was or is planning on doing, is to try to create conditions to dissuade states from holding elections, like inciting disorder with ICE, as he tried in Minnesota, to then use as an excuse to invoke martial law. A state could then decide, based on its own constitution, what to do in that situation, including postponing to some future date "to be determined" later.

Fortunately, public outrage is now such that I think there will be such a voter turnout that some of what he tried in 2020 -- calling state election officials and ordering them to "find him votes" like he did Raffensperger in Georgia -- is dead in the water.

Or to put it another way, if we keep protesting and showing up like we did in January, I don't think anyone at the state or local level is going to have the courage to "find" him jack shit, because they know they'll be facing a mob if they do.

Even Putin holds elections. He held elections in annexed Ukraine, too.

And holding elections at all keeps Trump's rule somewhat stable. If we know we'll get another election, "we can all vote a little harder to get him out". If elections simply don't happen anymore, then people may seek other means to remove Trump, like assassination.

not sure why you think that's "foolproof" - he has no authority to do that, and it seems tantamount to a coup to stop elections without constitutional grounds

Or just ignore the result. They might not be able to block every voting booth in the country, but they could easily block the newly elected Democrats being sworn in or even allowed inside the buildings. Then they start making laws without them. Who's going to stop them?