Jonathan Jordan recently did: he's losing, and he knows it.
While it's very common for a newcomer to challenge an office-holder -- Ron Zerban demands a debate with Paul Ryan, and Joe Rooney demands a debate with Allyson Schwartz, for just two of dozens of examples -- it's not common at all -- not at all -- for an incumbent to demand a debate. It's a glaring sign of weakness.
Challengers are usually not well known. A debate with the incumbent can get them better known in a hurry. In fact, just demanding the debate raises a challenger's profile, and the demand is often released to the press for that reason alone. Conversely, incumbents generally resist debates because they don't want their opponents to be better known. Simple math.
But for a well financed incumbent like Jonathan Jordan to be agitating in the public press for a debate sends a dog whistle: somebody needs to notice me and right now!
And speaking of how Jonathan Jordan has treated public education during his two years in Raleigh, which I believe we were, there's this.