As usual, Turkish politics is all about nuance. First of all, a coup benefits no one - previous coups perhaps brought short term "stability", but at the cost of the lives of many people jailed and executed without due process, and a lack of respect for the rule of law. They were pyrrhic victories at best, and set the stage for the current mass polarization of "secularists" and "islamists" that is causing so much unrest and strife. Back in the day, it also was "communists" once. Coups are not good or right, regardless of who they're orchestrated by. Lest you think
Lest you think the coups were mostly harmless, some examples of what happened were widespread (thousands) torture and arbitrary jailing, capital punishment, public hangings, repression of freedom of speech and books, purging of dissenting opinion from universities and government, special courts created to swiftly punish any opposition, repression of trade unions are just some of the results. Examples:
https://en.wikipedia.org/wiki/1971_Turkish_military_memorand... https://en.wikipedia.org/wiki/1980_Turkish_coup_d%27%C3%A9ta...
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Having said that, to the actual point: The right-wing secular generals have been dismantled for the most part anyway. The prevailing theory is that the coup might have come from the supporters of Fettullah Gulen, who's for some reason seen as a harmless moderate in the West, but in Turkey he's not. It's never mentioned, for example, that his organization in Turkey runs "houses of light" (isik evleri) which serve as alternate housing for students who can't afford proper housing, where young children are gently groomed and selected for religious coercion and indoctrination, to then join the organization for life. They're given proper educations, jobs, business connections, in return for their service of course. Perhaps the Gulen schools in the US don't engage in that, probably because they know that won't fly there, and Gulen is relying on the US's protection against the Turkish government. Also not mentioned is that they worked with the Erdogan government when it was dismantling supporters of secularity from branches of government. What makes you think that these people would make for a better leadership than the current one?
More about Gulen recently:
http://www.hurriyetdailynews.com/thinking-gulen-is-a-peacefu...
and also
http://www.al-monitor.com/pulse/originals/2016/07/turkey-cou...
Don't get me wrong, I don't like Erdogan and his group one bit, but a coup would not have been better by any measure.