It's not just feasible, it's existed for decades and is used by security cameras that record to (usually on-premises) DVRs. There have been open source apps that do basically the same thing (detect motion, save video around events, etc.). With modern mobile GPUs you have ample processing power for running over-the-top machine learning algorithms. There is no technical need to violate privacy by default.
The problem with the hobbyist approach (and this is coming from someone who owns multiple Raspberry Pis) is that you most hobbyist don't really have the resources to tackle every engineering aspect of building a reliable camera. We have people dedicated to fine tuning the WiFi drivers in the device, writing scalable and secure video storage/streaming services, figuring out the thermal profile of every component in the cameras, minimizing noise in the camera CMOS and the WiFi antennas, making embedded software that will reliably reboot itself after a catastrophic crash... etc, etc, etc.
Don't get me wrong, every one of those aspects is a lot of fun to tackle on your own, but ultimately would you trust your home to something you can throw together in a few weekends? After seeing the amount of work these guys put, I probably wouldn't.
...ultimately would you trust your home to something you can throw together in a few weekends?
With respect to the massive engineering effort, and acknowledging you probably didn't even realize you were doing so, I have to point out that this is an example of the extremely distasteful emotional manipulation too often used by security-related companies, and it needs to stop. Advertisements with lines of the form, "Would you trust your family's safety with anything less," or, "Nothing is too good for your children's safety," contribute to the general paranoia of society, not to mention the gross misallocation of capital based on manipulation instead of merit.
I'm the last person you'll hear using the "but think of the children!" tactic. American paranoia has been exploited for nefarious purposes long enough (I'm glad to say, I'd be surprised if you found any such message in the Nest Cam advertising campaign.)
Politics aside... it's your prerogative to buy or build any system you want. I was just clarifying why, in my personal opinion, if you really have a need for a security system, choosing a hobbyist project over a system built by a team of professionals is probably a bad idea (again, look for the article I linked before about how easy it is to "hack" into streaming baby monitors.)
> but ultimately would you trust your home to something you can throw together in a few weekends?
More than I trust it to something that sends it over the internet to someone else's cloud over insecure channels, yes.
"trust your home" is somewhat misleading. The house won't fall down if the surveillance cameras are off. I've been in that home for years now without surveillance cameras and it's fine; I'd be a bit happier with some video feeds in various places but it will contribute to additional security: It's not all or nothing.
Also, wi-fi isn't the only or necessarily the best option to hook it up. I did mention that storage is harder that image capture now, but I believe that a Synology NAS or similar is the preferred approach. Multi-Terabyte HDs have gotten affordable.