Given how ubiquitous your problem is, I would be suspicious that security alerts are going off because you have a real security problem. I've seen similar problems when a piece of malware keeps trying to inject itself into various things, and Gatekeeper is catching it. The variety of places where you're getting alerts is a testament to the persistence of the malware, and not the fact that everything is actually broken.

That's OK. If I were in your boat, I'd probably be pretty frustrated.

Does the method of right-clicking on an app, then "Open", in Finder work to tell Gatekeeper to quit complaining?

Probably the simplest thing then would be to alias brew install to something like spctl —master-disable; brew install $1; spctl —master-enable

`spctl --master-disable` requires root permissions (sudo).

You could edit sudoers so the command doesn't require a password. But really, at that point I'd just leave Gatekeeper off.

Is it possible you do this on a corp machine that has Google's Santa running & it's just a language precision issue? Google Santa will definitely prompt on nearly everything & is extremely annoying for Homebrew. Google Santa != Gatekeeper though.