It's fairly easy to abuse a state of exception to cancel elections. Ukraine has done it, and it's been, along with banning opposition parties and attempting to imprison critics (Arestovych, etc.), a critical step in their government consolidating power.
Ukraine's constitution doesn't allow elections when martial law is in effect. The US constitution has no such clause, nor anything else that would allow for delaying or canceling elections.
That's not to say it can't be done, but there's a huge difference in difficulty between doing what the country's constitution says, and doing the opposite. Especially in a country where elections are run by sovereign governments not under the control of the central government.
It’s absurd to claim that Ukraine (I’ll assume you actually mean “Ukrainian leadership”) is somehow “abusing” a constitutionally mandated state of emergency.