That would put the SCOTUS in the position of convicting a person without a trial, something that would be a violation of the 6th Amendment. Far more likely they would rule it's within the state's power to remove candidates from primary ballots.
The questions seem to raise an interesting issue: Are the 13th, 14th, and 15th Amendments restrictions on the states? Honestly, until today I'd never considered that, despite the 14th Amendment being used to apply aspects of the 1st to the states. If so, they may argue that states could bar someone by the provisions in the 14th, but then we're right back to conviction without a trial. It will be interesting if the SCOTUS rules that Colorado has to remove people guilty of insurrection or rebellion from ballots, but that Trump has/had not been convicted and thus could not be removed.
Really, I'm surprised by the questioning. I thought they'd leave it to the states. The questions do raise some thorny issues.