Why doesn't any company make a camera whereas it records to a server rather than directly to the device?

Apparently you have never heard of facebook live.  I believe there are other cameras on the market as well, but you need an internet connection that you are going to get on a government base, except via cell phone signals.   Government facilities make you leave your phones and cameras when you enter, not just when they think you might have take video.

boh............. 

Recording in the server demands for Internet connectivity, those too high-speed ones, if the image file size is large. It is a tough requirement to meet in all situations. That is why companies don't prefer this method.

You want a wifi camera, or an IP camera. Digital cameras contain NO FILM.

And your expectation for the connection between the camera and the server is... "the internet". And to get to the "the internet" to get the video to "the server" the camera needs to be on a network connected via wifi or cell phone data plan.

If the activity being captured to video is that big of a deal, then the cell phone signal will be blocked and wifi access will be via password - if there is any wifi coverage.

The only thing expected to be more reliable than hoping cell phone or wifi coverage is available is knowing local storage is available.

But... to your point, most of the "IoT" security cameras already send to cloud storage (assuming wifi availability), no local storage. See Ring, Blink, and dozens of others. Cell phones can send to cloud storage or store locally.

One of the big issues would be the bandwidth. Do you expect every single camera owner to pay for a mobile Internet connection so that their footage gets backed up? Is the company going to pay for it or what? What about very large video files in the tens of gigabytes? What about when you're in remote areas with no Internet or very slow connections? How is the company going to pay for the storage? Are they going to charge the user for storage?

And what about the people who aren't comfortable with putting their pictures on the cloud? Haven't you heard of all of the data breaches that have been going on for years? Big companies that are supposed to be "secure" and "safe" are usually incompetent when it comes to network/data security.