That's pretty standard in most places AFAIK. Think about it - apartment salespeople are mostly women. Potential tenants are at least half men. When you walk in off the street to look at an apartment, they don't know you from Adam. And you're going into an empty apartment alone with a female salesperson. Do the math, they're gonna want some ID first.
Deterrence. Having your ID on file (vs knowing only a name that they likely made up) makes a potential criminal much more likely to get caught, so they're much less likely to do anything bad.
