Our swat teams have paramedics and I believe a doctor or two. If our swat guys are doing a warrant it's for a violent person. So fire is staged nearby. We also have fire/PD liason units in my department. Thats' thir entire job. But being a bigger dept in a big city, we have more resources that smaller departments. But no matter if you got fire/EMS staged or not, they are not rolling into a hot scene. Some crews who work in the bad parts of town do sometimes, but it's not the norm.

On the other hand, Ive been on a few search warrants with the FBI. Never worked with one of their full time swat teams (who I hear are legit) but have been around their field agents who went through swat training types. Every warrant I went on was a complete shit show. Planning was bad, tactics were bad, it was just all bad.

Like was said above, in a normal PD your investigators have years of experience on the street dealing with bad guys face to face. The FBI agents are good at investigating but their interview skills, safety, and tactics when they are actually out on the streets are lacking. It's actually kinda funny watching some ivy league college graduate try to interrogate a gang banger whose robbery crew decided to try doing banks.

Now, that doesnt mean every FBI field agent is a bumbling dork and every PD detective is a badass. We got plenty of detectives who went to the desk to get off the streets because they were bad cops or were scared and wanted to get away from patrol work.