I think that ship has sailed. “Edge computing” is a well established phrase at this point. When I need to refer to the scenario you’re describing I usually say “local computation”.
If that's were the case, why would the entire first page of Google search results for "edge computing" refer to IOT, and processing data where it's created?
You’re right of course, IoT is edge computing because it’s treated as company’s edge, while we can’t say the same for end users’ phones and computers.
But that's only because there aren't any compelling IOT applications in the consumer space. Companies are the users with distributed assets, not consumers.