Here in Colorado we have the dubious honor of suffering through two of the worst mass shootings in U.S. history; Columbine H.S. and the Aurora Theater shooting.
At Columbine, PD was one scene within a few minutes, but did not go inside the building. They waited for SWAT to show up, before entering the building. This gave the two shooters (I refuse to mention their names, or any other mass casualty shooter, giving them the fame they crave) time to enter the library and inflict the most damage. Once SWAT arrived on scene and penetrated the building, did the two shooters then take their own lives.
It was because of this incident and the incident at Platte Valley H.S. in Baily, that PDs here in Colorado (don't know about the rest of the country) changed their tactics when involved in an active shooter incident.
Now instead of waiting on SWAT, LEOS are now trained/given the green light to enter the building/area and neutralize the shooter, if possible. This was the case in Aurora.
Granted, the LEO station was less than two miles away from the theater, and when the first 911 calls came in, PD was on scene in a matter of minutes. They surrounded the building and had actually entered the theater, but had to pull back out due to the home made "gas" that that shooter had deployed.
This shooter hadn't realized that PD would be on scene as quickly as they were, seeing that he hoped that his improvised explosives that he had in his apt. would have distracted the PD enough that he could have gotten away, as was almost the case. He in fact, almost did get away. He had just exited the theater out the back and was noticed by several LEOs who were securing the back. The LEOs thought he was SWAT, seeing that he (the shooter) was dressed as one; tactical clothing, body armor, k-pot, gas mask, ect. It wasn't until one of the LEOS radioed command asking if SWAT was on scene, that they were told that SWAT hadn't even left the station. It was then that the LEOs in the back did a 180 and secure the shooter.
The problem with the Aurora theater incident was coordinating the other responding assets (EMS and Fire).
IMO ... SWAT teams are over rated. Yes, they provide a valuable asset to the mix, but to use them as they have been/are being used is just short of the U.S. becoming a militaristic country.
As has been mentioned, NASA, Dept. of Fish and Game and the Education Dept (

) as well as several other govt. depts. all have SWAT teams. This not only borders on the absurd, but crosses into the realm of, "You've got to be fucking kidding me". Next thing you know, anyone who is on a PDs SWAT team will want to be wearing berets.