Democracy has nothing to do with it - it's just a convenient stick they can use to beat the dog. If the electorate is dim enough to believe the sceptics have any interest in democratic accountability, more fool them.
Elected leaders are hardly models of excellence - Blair, Aznar, Burlesquoni, ad nauseam - so being elected isn't quite a benchmark of appropriateness.
What this debate underlines is the impossible criteria needed for leadership. If you're elected you're likely to be a spiv, a fool, and/or a sociopath, and if you're unelected you're undemocratic - which is even worse
