>>if there's a majority of Turks who support the regime, what's the problem?

There are at least two problems.

First, the "will of the people" argument works only if there is a strong culture of democracy, respect for the rule of law and proper representation of minorities. None of those things exist in Turkey (I'm Turkish). Typically, what happens when Erdogan wins elections is that he views it as a "mandate" and starts oppressing the shit out of his opposition by jailing or exiling people who disagree with him. He has gone so far as to use his party to change laws in his favor. And all those infrastructure improvements he has made? They have all enriched himself and his buddies (called "crony capitalism").

Second, Turkey is an extremely important player in the Middle East. If we want the region to stop spiraling out of control, there needs to be a modern, stable and secular democracy with a Muslim population there that can be used as a model by other countries. Otherwise the region will always be in turmoil, which will inevitably spill over to Europe and the rest of the world (in the form of refugees, extremist terrorists, etc.).