My thing is that I get so many callers who are really bad at making a determination for themselves what is and isn't an emergency or who to call. They'll call a 10 digit police non emergency line because someone's having a heart attack or their house is on fire or something else really urgent instead of just calling 911 or even instead of calling the fire department or ambulance station, or someone got stabbed and they call the wrong towns non emergency line, maybe even a town with the same name in a completely different state or even country (I once got a call for a town in Australia with a similar name to one of ours) so we kind of have to act like those non emergency lines are also potential emergencies.

Yes, they do go to the back of the queue, and in some places that's more of an issue than others. In my jurisdiction, if the phone rings 2 or 3 times before it gets answered, emergency or not, that's a lot for us and we've been fortunate that our staffing and call volumes haven't been bad enough for that to really come into play except for some really bad major incidents (mostly severe storms and such, in which case, most people aren't bothering with non emergencies anyway)

Some places do have longer queues and it could come into play, but I've had to transfer callers all over the country, usually those transfers end up going through on a 10-digit non emergency line because of how the transfer works, so we're going to the back of the queue, and it's pretty rare that we have to wait long for an answer. It's less of an issue overall than you probably think.

Those non emergency calls can also often be handled very quicky. For a basic non emergency call, I'm getting an address, name, phone number, and like 1 or 2 short lines of notes, I've entered probably thousands of meet complainant calls (officer just needs to go out and meet with the caller to take a report) where the only thing I put in the notes was "RE: FRAUD," "RE: HARASSMENT," "RE: ONGOING ISSUE WITH NEIGHBORS, NOT IN PROGRESS" etc. If the caller is even marginally cooperative and not too long-winded it can take me like 30 seconds, they're not tying up the queue for long.

One of our neighboring counties does have staffing and call volume issues, and it's not uncommon to have to wait a minute or two for someone to answer, and sometimes even longer (they got hit hard during the George Floyd riots a few years back, and a couple times I had transfers to them during that that had we wait like 10 minutes in the actual 911 queue)

But a lot of the callers for them tell me that they tried calling the station directly or 311 only to be told to call 911 instead, even for some things that our stations could handle directly (and again, ours can't handle much)

Location is also a big thing, having a landline address or cell phone location is a big time saver and we don't get that on non emergency lines. A lot of our callers have no idea where they are, what police department covers their area, etc. (you'd also be amazed at how many people don't know their own home address) and so a lot of times just trying to verify the location where something happened/is happening is the longest and most difficult part of the call.

It's also sometimes surprisingly hard to find local contact info. Even with access to a database of other 911 centers, Google, etc. I've occasionally struggled to find the contact info for some other jurisdictions when I'm trying to transfer a caller, once or twice I struck out from the usual channels and had to call a neighboring jurisdiction and ask them to be transferred or get the correct number from them.

It pays to be aware of any special situations in your area, if they do have high call volumes, staffing issues, etc. and calling with a non emergency can actually create significant delays

Or we have a couple departments that have chosen to opt out of using our county PSAP for police dispatch (although we still handle fire and EMS for them) so in those areas it is often preferable to call them directly instead of needing us to connect you to them, although that location info is still very useful and again they don't get it if you call them directly, so there's been cases where someone calls them directly, but can't tell them where they are, and they end up telling the caller to call 911 so we can get that location info for them.

But at the end of the day, the point of 911 is that no matter where you are, even if you don't really know where you are, you know what number to call to get in touch with police/fire/EMS. Hammering on people about what is/isn't an emergency is kind of antithetical to that, and overall most areas are moving away from that.

If you are absolutely certain that your call isn't an emergency, you have the time to look up the phone number, and you're ok with very likely being told to call someone else, or call back at a different time, maybe getting transferred around a few times, etc. then by all means please try the non emergency line. If you're not sure, if you can't wait, if you don't have the phone number, if you need a cop to go do something now, then probably call 911.