Democratic Islamic state is an oxymoron.
It is impossible for an Islamic state to be a functioning democracy. Within a very short time, the concept of free speech gets shut down, and nothing like the Bill of Rights, as inscribed in the US Constitution, is ever allowed to be enacted. Shari’ah law provides for no mercy, no appeals, and no justice. It is purely a punitive code, and the penalties are spelled out before any judgment or even the accusations are announced.
Recep Tayyip Erdogan is a True Believer in the efficacy of the Koran, and is in the process of implementing the measures outlined in that tome.
Kill the Armenians.
Kill the Kurds.
Make sure the influx of fighters for ISIS get free passage back and forth across Turkish territory, providing sanctuary as needed.
Accept all the black market oil ISIS is stripping from the producing wells in territory they control.
Bottle up the Americans until such time as they agree to no longer attack ISIS.
Resist efforts by the Russian Federation in establishing easy passage to the Mediterranean, and a large-scale presence in Syria. This includes air passage.
The purposes for allowing this coup attempt to occur lay mostly in an effort to smoke out the leaders of the coup, forcing them to act too soon and destroying their initiative. Both Adolf Hitler and Josef Stalin used similar tactics while tightening their grip on the reins of power in their respective countries.
You raise a lot of great points but on this one fine point I would say - not necessarily. The U.S. voted for Obama twice. People can vote for abhorrent forms of government. I have no idea whether the Turkish election was fair but given the country is 99.8% muslim it is certainly possible that those muslims voted for Erdogan and I could see muslims voting for an islamic government. People can do some stupid things. I raise this not to quibble with you but rather to point out how fragile our freedom is over here.