Does anyone know if anything like this, but for emergency vehicle responses? In some cases, routes that are not suitable for a normal car are exceptional quicker for an emergency vehicle to use (because perhaps they can do a right turn at an intersection that normal traffic cannot).

There would be restrictions, because you wouldnt want to go down a wrong way street etc, and some "no right turns" have physical reasons etc (such as median strip that would physically prevent you from crossing).

But there would definitely be a market for this to improve response times. In my country at least (Australia); most emergency service vehicles I know of use a standard GPS routing system that does not take this stuff into consideration...