Perhaps the state can continue to function without an effective head of government if Kim Jong-un proves to be a lame duck. But factionalism in the government, in the military, or in some cross section of both could boil over into an all out power struggle without some arbiter (like the "Dear Leader"). Of course it is widely speculated that Kim Jong-un's Uncle is the real power behind the throne, but we have no idea how secure his position is. As you point out, Kim Jong-un's only qualification to the throne is ideological; North Korea is not a monarchy. Certain generals may decide they are tired of taking orders from lunatics.
Why would they consider the Kims to be 'lunatics'? I strongly doubt anyone within the upper echelons of the KWP feels Kim Jong-Un shouldn't take over, especally as he appears to have the PRC's blessing.
