And how did the work out for the british in WWI? They could have invested in tanks and used the Blitzkrieg one war early, but the officers loved their horses. Using horses was not a sign of health, it was sign of backward thinking and nearly cost them everything.
It was necessity for both sides, because of limited infrastructure, fuel supplies, and priorities in manufacturing.
Most horses were used for logistics if I recall.
It was because that's how they had always done and the idea that real soldiering is on horse back. It was culture, not practicalities.