You said "...bicycles are worth the time and effort for insurers to launch full investigations over."

and I said:

"I would agree, yet I have seen it happen."

I was precise in answering your precise statement.

I have seen claims for less than $5000 items create significant investigative and delay-inducing efforts from an insurer. A video of the theft would have, in some of those cases, reduced that effort. Having video evidence is in almost no circumstances going to increase the time it will take to get an insurance claim paid. By you having the video evidence, you have the choice if you want to disclose it. It is just upside that you control.

If you do not want to put a camera in your garage pointing at your mountain bike, by all means do not.

Just like there's an imperfect but effective barrier to lying to the cops for a police report, there's an imperfect but effective barrier to staging a theft on a video camera.