First of all, I assume you meant to say non-residents, rather than non-citizens.

Second, the obvious pitfall here is that tourists don't like feeling like they are visiting a tourist trap, and openly charging them different prices makes it seem like one. I've visited plenty of sites that charge significantly more for non-citizens (in India, in this case) and it feels more exploitative than paying a fee in a country that does not do this. Some museums in Spain, for instance, reach a middle ground by providing free admission to EU citizens during a low-traffic time of the week.