In truly emergency communications, I don't see a lot of value to APRS.
But for public service events, like marathons, bike-a-thons, etc., it's pretty useful. Say that runner XYZ is at mile marker 18 on the marathon course, and can't continue, requesting a ride back to the start/finish. If you're the net control and your SAG vehicles have APRS trackers aboard, it makes it very easy to identify the closest SAG to pick up the runner. It's a big help in providing the requested support in a very timely manner, without tying up the net to obtain position reports from all the SAG vehicles on the course, while trying to figure out who to send. Likewise with medical units. If someone gets hurt and needs medical assistance, APRS makes it much easier to know who the closest medical unit is to an incident involving injuries. It enables you to get medical assistance to an injured participant much faster.
If you're working a parade, if you embed an APRS equipped ham in the first and last units in a parade, it enables you to see how the parade itself is progressing along the parade route, in more or less "real time". Since street closures and their duration for a parade are usually specified in the parade permit, it lets you open up the streets along the route after the last unit has passed, which returns disrupted vehicle traffic to normal quicker than you might be able to otherwise.
When we work such events, our net control position is usually located in the city's emergency operations center. The benefit to that, is that we get direct access to law enforcement and other support functions, and the operations staff gets real time access to event communications. Comments we receive from operations staff frequently indicate that they get better situational awareness from listening to what the hams are saying, than they get from people who get paid to work an event, like police officers and sheriff's deputies. We often get operations staff poking their heads inside the radio room, to check out our APRS computer display. They are often amazed at the "technology" that a bunch of unpaid volunteers can bring to bear on events like these, even though to us, APRS isn't really that big of a deal.
If you usually don't do this kind of thing and are wondering what a SAG is, SAG stands for "Support and Gear". We usually have 6-8 (or more) vehicles that provide support in a decent sized marathon, and another 6 or more medical units. Medical units could be private ambulances contracted to an event, or even municipal EMS units who are assigned to an event. The actual number varies with the size of the event, and how spread out the course is.
Of course, your mileage may vary. But these are my observations and experiences after having been involved with such things for over 30 years.
73 de N8AUC
Eric