But there were more Orthodox besides Byzantium...
Why did the Russians never make one of their wars with the Ottomans about reclaiming Constantinople? Too difficult?
If you mean the Russians, then their medieval church was even more anti-militaristic; additionally the Princes mostly fought defensive and internecine wars in the middle ages, with the exception of raiding and counter-raiding with their steppe neighbours (Cumans etc.)
That was actually frowned upon, and even princes underwent penitence for waging wars (for example, barred from communion for a time until repentance is complete). It was generally a little better for them when they managed to beat up pagans rather than other Christians, and there are a few warrior-saints. However saintly peaceful princes outnumber them in the canon by a very wide margin.
That said, yes, things could potentially change, but it's not an easy goal to accomplish using modest PODs.