only true up to a point
If it was only about flag and footprints, why have 6 manned landings - each more in-depth exploration than the previous one?
Dave Scott (Apollo 15): "man must explore"
Your point about ego is valid, but not the whole truth. There's a transcendental aspect to space exploration which we seem collectively to have forgotten - and which obviously touched both the Americans and the Russians back in those days. The ego aspect then kicked on from there - but it wasn't the basic prime motivator.