I think usafmedic is probably right here.
I will say that on several occasions I have entered the scene for these calls without the cops, because the information from dispatch has been reassuring, e.g. parents upstairs found son unresponsive after self inflicted long weapon wound to the head, wife found elderly husband with transoccipital wound in garage, etc.
But these have been unnecessary risks on both occasions. We tend to give ourselves a little too much importance in these situations. If you've just witnessed your teenage son, or your husband of 50 years kill themselves, or the immediate result of this, that your biggest problem. While a delayed EMS response might add to the agony a little, and it might be something the family choose to fixate upon, it's not even remotely close to the primary problem in this situation. The aftermath of this decision might not be nice when you arrive, but, then again, they may reasonably accept the police responding first (especially if PD response is rapid), and, if they don't, responding to a suicide call isn't about the emergency responders feeling loved and cherish. If we have to absorb a little bit of someone else's anger, at least it's for a good reason.