How can the strongest army win a war when the individual soldiers don't believe in the cause they are fighting for?

The High Command cannot Orwell the information space forever. Eventually The People will find out what is happening and go apathetic or worse: join the enemy.

Genocidal rhetoric towards the enemy also backfires enormously in the Information Age as it makes them fight to death and refuse any de-escalation. From their perspective, any attempt of deescalation will be for short-term repositioning, not for everlasting peace.

All of this has happened before. And will happen again.