I know for a fact that hesitancy to enter and engage happened during the El Paso, Texas Wal-Mart shooting.
I got a first hand account from one of the first men to go in about an argument at the front doors with an officer with a carbine not wanting to enter and not wanting to give his carbine to another officer who was entering.
Hesitancy was not a factor in the Alpine, Texas school shooting response. Again from a first hand account relayed to me, "blue on blue" was a serious concern because of the overwhelming immediate entry by multiple agencies. Alpine's strategic location near the border means there are a lot of local, state and fed LE there. There were some other issues in Alpine with clearing rooms and the evacuation of teachers/students, but none that delayed the initial entry.
I don't think there is a perfect response to active shooters, but in such a chaotic situation there never will be.
The best that can be done is improvise on the spot with the immediate termination of the threat being the only priority.