It would be great if you could call animal control for every time you had a call where an animal might be involved. The reality is too many time the situation is fluid and fast-changing and there is simply no time.
Some years ago my Sgt. and I were dispatched to a domestic and upon getting out of our vehicles, and starting our approach to this unfenced house, a pit came charging around the corner from the back of the house, full speed, bone in teeth, figuratively. My Sgt. was ahead of me, and had only time to draw and fire twice while trying run backwards. First round went between the pits legs, second went into his chest as he was lunging on my Sgts. right thigh. That round was fatal but not instantly incapacitating because he ran off back where he came from and died under the back porch. The owner was not happy but understood that it was his responsibility to keep the dog secured. A ticket was written, a complaint was made, in the end both went away.
The point is, we had no time to call animal control, and in the SWAT scenario, they simply could not put an animal control officer in the line of fire. An animal control officer would not want to be there either. Unacceptable risk.
We officers cry too when our K9s are killed in the line of duty and have funerals for them. You have to be particularly attentive to K9 officers when they lose their partners. They get really depressed and some have committed suicide over the loss of their partners.
I would desperately like to see another method but it’s just not there at this time.
Like I said before, I couldn't do your job. But, I'm usually grateful that you and others can and are out there 24/7.
But...some of these stories simply undo all the goodwill you've earned and that can take forever to repair. I hope some new technology or additional training can give you better options in some of those circumstances.
I don't want to be afraid to call you if I truly need help.