> There are already large numbers of Turks in western Europe, particularly Germany

Define large numbers. It's around 5% or even less in Germany which hosts the biggest Turkish community to the best of my knowledge, and way less in other European countries. Bringing Turkey in imo might dissolve the Union, I don't see anyone trying it soon.

> Turkey refuses to address its past with the Armenians, Kurds and Greeks which is a major concern.

It's also a dictatorship and its population is probably not in favor of liberal democracy - most (all?) Muslim countries aren't.