Speaking as a simple country bumpkin who has limited access to the internet (Wild Blue or 4G cell), I know that connectivity is not guaranteed at any time or for any duration. The only thing I would consider reliable is that which is local.
Remote storage and processing are nice, I just have trouble trusting them.
Your skepticism is mostly justified, when it comes to our typical consumer endpoint access. But the servers out there are surprisingly robust, and the connectivity is generally very good (major backbone outages aside).
These little server instances won't replace the big honking local network machines that do yeoman duty for a corporation -- those do indeed have to be local. But services that can be effectively put into the cloud, for employees who are traveling, or working at home, or for the general public, will benefit from lightweight server platforms like this.
Also, the small size and subsequent small cost means that it now will be economical to put things in the cloud that would go well there but cost too much if the server platform was the big honking one we grew up with.