strong apolitical candidate
They would have an even worse chance of winning than Jeffries.
The Speakership is not an award or purely ceremonial position. The Speaker is a political operative. Their job is to unite a majority and keep it united during subsequent legislative votes. Winning the gavel is just the first test. If they can't consistently get a majority to vote for stuff, their gavel is useless.
That's why Democrats won't vote for a GOP Speaker unless they strike some sort of bipartisan deal about future legislation. In other words, Democrats will support whoever can offer something to Democrats in exchange.
An apolitical outsider offers nothing to anybody. They have no chance at becoming Speaker for that reason. And if they accidentally stumbled into the job, they would be unable to pass legislation - so why bother giving them the job?