That's not entirely the case. I've been running internet-visible servers from home for decades. My current ISP (Comcast) doesn't have a problem with that, even contractually, as long as you aren't running publicly available services, and I've never had a problem with any of my prior ISPs.
Most ISPs don’t seem to care if you’re not using a ridiculous amount of bandwidth. Many will sell you a package that explicitly allows it. I currently have access to live view and recorded video from my security system and haven’t had any problems at all.
In the case of wide adoption of such a thing I imagine the ISPs either offering a more expensive package, or clamping down and offering their own version of the service through some monstrosity of a modem/router. It’s probably the latter that motivates most of these companies to use “the cloud”. There’s certainly ways around the problem for a motivated company, though.
The ToS says you can't, but it isn't enforced.
Yes. Plus ISPs (or at least US ones) won't allow you to run an Internet-visible server using your home Internet connection.