I’m not against an EU military in principle, so my question isn’t loaded, but genuine curiosity. What would prevent an EU Army from possibly forming a corrupt military leadership?

It's a good question, and probably has no good answer.

As it is, a current corrupt European military is constrained to a single nation, and would have to coup that nation before conquering the continent. There would be no such natural constraint for a unified EU military.

And when Germany is no longer satisfied with Greek loan defaults due to the Greeks simply not taxing their population? Do you think that Germany will let Greece tank the Euro without exhausting every option on the table, including replacing Greek politicians if necessary?

If this sound far-fetched to you I implore you to look at the last decades' relations between the countries.