As I've written a large explanation, here's the abstract of my suggestion:
-add option for players to allow casualties to "deteriorate" in missions
-deterioration would be slowed as more paramedics arrive
-some missions deteriorate faster than others
-make casualty missions have "expandable missions" like fire & police missions do
-casualties can become "deceased"
-fire and police missions can also have forms of deteriorating
So this suggestion could be relevant to all servers, but I'm from the UK one, and my suggestion is to add a new feature where on casualty mission, the casualty will 'deteriorate' overtime while paramedics can't get to them. Obviously it would best be done as an option for a player to change, so an added option button saying 'allow casualty deterioration' or something of the sort, that way newer players are not pressured by a time limit to begin with.
I believe this sort of feature would add a lot more realism to the game, as one does not just leave a casualty in cardiac arrest overnight and expect them to still be there in the morning! To further the feature, deterioration could be slowed down as paramedics arrive (critical care and HEMS trained personnel could slow deterioration more than untrained personnel). This would really amplify the use of rapid response vehicles and community first responders (in the UK), as well as would potentially require multiple ambulances to turn up to 1 patient (which is how it can work in the UK). Certain incidents could have faster deterioration rates than other: so "nose bleed" although could warrant an ambulance for an old dear who often they will not stop bleeding through the nose, it would be a slow deterioration rate compared to "cardiac arrest".
So as the casualty actually deteriorates, the sort of thing I picture is an added bar, similar to the bar that falls down as the casualty is being treated. If the deterioration bar falls completely, it could escalate as such to a more serious medical mission, basically making medical missions having "expandable missions". Some examples could be "acute asthma", "chocking" or "anaphylaxis" when completed deteriorated leads to "respiratory arrest", "fallen person" when deteriorated leads to "hypothermia" (new mission there for you) "electrocution", "chest pains" or "seizure" leads to "cardiac arrest". The more serious calls such as "cardiac arrest" "respiratory arrest" "traumatic limb amputation" etc., if they deteriorate (which they would quicker) then the casualty would become "deceased".
You could even carry this sort of deterioration feature over to police and fire too. Where say "bulk rubbish fire" or similar missions expand into "garden shed fire", a deterioration bar could be added to these incidents to show how quickly the fire is 'spreading', or with police in how quickly a "noise complaint" mission is 'getting out of hand' into a "brawl".
Let me know all your thoughts! Please feel free to expand on this,