> They will even ask you this if you say you're on 3rd Avenue
"4th street and 3rd ave" is a unique identifier. The East/West part is only relevant if you give the street + a house number, with no cross-street.
I'm not sure if the op used it as an example for this reason or am I being overly pedantic but... there it is.
Remember that not everyone who calls 911 in New York City is a local. In fact, given the tourism in the city, I suspect a large fraction of 911 calls are from non-locals (a local is gonna walk right past a drunk sleeping on a bench... a visitor might call it in as a "person down").
Verifying the location of an emergency is literally step 0 in dealing with it. Spending 10 seconds asking some "dumb" questions to rule out confusions that have come up in the past can save a significant amount of time overall.
Why is that an unreasonable question? People calling in emergencies are generally stressed and often very bad at accurately communicating where they are. A few clarifying questions, even if they don't make sense to you, can go a long way towards verifying the information they're being given.