Agreed. And it can be even worse than that. At one time, my county (Brunswick County, NC) had three separate dispatch centers: the primary county 911 center, then a Southport specific dispatch center, and then a Long Beach specific center. And none of the agencies involved had any kind of integration of their systems (radio or CAD, etc).

That has improved somewhat now (everybody is dispatched by one center now, and everybody uses the NC VIPER radio system) but the point remains that most dispatch centers aren't integrated with each other. The CAD system for one county doesn't "know about" incidents happening in neighboring counties, or anything. They are generally almost completely isolated islands, with the primary means of interop being telephone calls from one center to another to request mutual aid or EMS move-ups, etc.

So yeah, expect it to be a while before there's any meaningful integration that can be expanded to include private companies or other 3rd parties, when the dispatch centers barely have any interop between each other.

When someone dials 999 in the UK, the call goes to the 999 handling centre where it's directed on to the appropriate agency (Police, Fire and Rescue, Ambulance, Coastguard etc - often one will pick it up and then bring the rest). Both the 999 receiving centre and the agency that the call is handed off to get the location of the caller, but only if it came in via a 999 line, got handed over via a "999 to agency" line, and then over a special dedicated connection that you most definitely do not have.

I'd expect that for something like self-driving cars it'd use the opposite of "Greenwave" which will adjust green light timings on routes to suit emergency vehicles. I know that city buses where I used to live also had Greenwave and would update their control room with their GPS position, which would then "nudge" traffic light timing to speed them up or slow them down so they ran to schedule.