So, what makes "ruler by popular right as acknowledged by election" greater than "ruler by divine right as acknowledged by coronation ceremony"?

Coronation ceremonies are too easy to fake.  Or, rather, too easy to duplicate.  Any pretender can put one together, and probably it’ll have most of the compelling power of the true article. 

…that’s the glib answer.  The slightly-less-glib answer is that, while in an abstract sense (I posit) it doesn’t matter what the legitimacy criterion is so long as it’s unambiguous, in practice it does actually have to get some cultural traction in order to serve its purpose.  Things like “being crowned by the Pope” and “being the eldest son of the king” have reliably failed in this regard; they don’t protect you from coups and intrigue, because no one really takes them seriously in the right way.  It’s not unacceptable to depose a king-chosen-by-primogeniture via force of arms, no matter how hard various kings have tried to make it so, because in the end it’s hard to spin your particular lineage as mattering in any very profound way.

(Interestingly, the one sort-of-counterexample I can think of is the imperial line of Japan, which – despite some turbulent periods and nasty intrigue – is in fact treated as an unbroken divine bloodline that really does matter, or at least has been treated that way for a very long time.  I suspect it is not an accident that for much of that time “Emperor” has meant “sacred figurehead” rather than “wielder of supreme political power.”) 

“Legitimate authority arises from the will of the people as expressed via elections” is stupid, in the sense that basically no one actually gets to see his will expressed that way, but it does make for a sticky meme and people believe in it.

I assert that people are also willing to believe in credentialing systems.