I think the religious zeal is part of it, but we must remember a few other factors as well. The major economic component of colonizing the New World essentially demanded the Spaniards enslave the natives, which they did, and leaving the vestiges of their empires and pagan symbols was unnecessary, if not outright harmful, to such a goal.

It should also be noted that at this time in history, looting and pillaging was an accepted part of warfare, and was a significant chunk of how armies kept fed and supplied, as well as being a vital way in which soldiers secured a profit from going to war, and that is when we're talking about inter-European conflict when both sides are White and Christian; against pagans, especially ones of a different race, and even more especially when we take into account the horrific brutality the stone age savages of North and South America were (and are) capable of, it stands to reason that the Spaniards would not hold back in their destruction and pillaging.

really, there's not too much difference between this and what happened in Africa 200-300 years later, the main difference being that the conquest of Africa was much more recent and in a time where scientific documentation was considered more important.