If they can get the data to their server to store it, they could just as easily not do that and instead serve it from your local device by proxy through their server.
It’s t he exact same difficulty as what they are already doing. Arguably easier since you don’t have to manage file storage in the cloud.
Could you please stop posting unsubstantive comments and flamebait? You've unfortunately been doing it repeatedly. It's not what this site is for, and destroys what it is for.
Do you think they use magic to stream live video with today’s implementation? It already works. We stream HD video out of our homes all day every day, and that includes video from security cameras.
If the devices can stream live video, and they all can, then they can stream stored video.
As to why they would do that? Online storage costs money. Some users are not comfortable having their videos stored with Amazon. Plenty of good reasons.
This isn’t some lunatic idea, local storage is literally how ALL security cameras used to work, and there are products that do exactly this. They have good reviews too.
In practice it's difficult to do and offer remote access.