The assumption that it will wash away in the rain rather than find its way into cracks and pits in the rock is an awfully big bet to make vs permanent damage to history.
Cool. So you'd be fine with me coming over and spray painting something of my choice on your house, assuming I assured you (with absolutely no supporting evidence) that it would go away over some unspecified period of time?
I do not think so.
Anyone who's been around small children knows that some food dyes do NOT disappear when washed, even with detergent.
