It's not a standard capability yet, but Hubitat seems to be using a custom networkStatus attribute on newer drivers to represent some statuses like this (for example, telnet, where this is actually part of the capability; and an upcoming LAN device integration app that you'll see when 2.3.3 is released). A few community drivers have used presence for this in the past due to the lack you noted; I would not suggest that, given that it is intended for physical presence devices and can be confusing for users to see unexpected devices in apps that want to use that kind of device.
My suggestion would be to follow this convention and use a custom attribute, probably networkStatus, though since it's custom (usually), it doesn't really matter right now. Maybe some day it will be standardized. What you've suggested is probably also good, then if it ever changes at the platform level, you could adjust if needed.
But the Rule Machine issue is a separate one; while the dropdown lists some of the most common capabilities and the "primary" attribute most people would want from them (e.g., motion for a motion sensor), it doesn't list all of them. Using "Custom Attribute" in a trigger or condition is still necessary even for some standard/capability attributes, and it's only a couple extra clicks. Even if such a platform-level attribute is added doesn't mean Rule Machine would make it easier to get to.