I live in a busy city area too and not far from a large city hospital (and Moss Side) so lots of emergency services around here.
They often take alternative routes such as quieter into city sides of the road rather than busy rush hour right side of the road for instance. They are very noticeable though and slow by junctions etc... to be safe.
If they are well trained, safe drivers then I don't see a problem. If I needed the emergency services urgently then I'd be grateful for the quick response (and, indeed, have been).
Some emergencies can be time critical, people who have stopped breathing or bleeding seriously, heart attacks etc... and the speed of emergency treatment could mean the difference between life and death.
I see loads of emergency services day in and day out and can't think of an occasion when I've seen any of them driving what I'd call dangerously, buses and cyclists and general drivers on the other hand... I've had two very close calls being on a bus with idiot drivers (car drivers in this case) in just the last week or so.
If the accident rate was high then there would be more cause for concern. I know there have been incidents, especially people hit by police cars on emergency calls though I assume there were enquiries considering the circumstances and individuals involved and action was taken. Just because one driver makes a mistake, doesn't mean the whole lot are at fault.