Dragons maketh King part ?

A dragon is armageddon incarnate. Fire made flesh. Power in its most natural and animalistic state. A being that can obliterate any other type of being through will turnt action. To control such power means to wield a literal weapon of mass destruction. Scales that make the finest armor, a brain that, through sheer size, makes it smarter than most anything, and a mouth that spews all-consuming napalm, make the dragon a living, breathing weapon, if controlled. A weapon that steers at your command and attacks at your behest. A weapon so powerful that, if handled properly, would make any peasant's son atleast a regional warlord, even without an army. Armies, of course, are a fine thing. They are and have been the modus operandi for any greater conflict between parties since time immemorial.
The lord of Dukington called me a what? RAISE THE LEVIES!
This boils down to the so-called "bigger army diplomacy". Pretty self-explanatory, but nonetheless it should be noted that only having a bigger army in numbers does not balance incompetence. Only incompetence balances incompetence. Strength in numbers can be balanced through better equipment, positioning or intelligence.
A dragon throws most of that out of the window. Having an intuitive helicopter that shoots napalm, allows for different tactics. For one, it allows for purely one-sided "assured oblivion threats".
Do as I say or your lands will be deserted and uninhabitable for millenia.
That is a much more potent threat than "do as I say or I will besiege you and give you battle if you're offering".
Under the right conditions, a dragon is a tool that not only maketh you king but maketh you a mortal god. However, gods don't rule kingdoms, which puts that idea into the basket of "pure megalomania".
Any man, that finds himself in control of a dragon, can turn his farm, his holdfast, his city mansion into an empire for himself, provided unforeseen circumstances do not strike unfortunately.
He can even call his empire by himself, provided the dragon isn't sentient.
If the dragon is sentient now, then you have most likely unleashed judgement day upon all.

Take care