Actually if you phrase it like that it actually makes more sense now. What most people want to run is Hass.io (which like me was confusing to understand when you’ve never heard of hassio but have heard of Home Assistant). Basically what I wanted to use all along is hassio (like you say the full package). But we all call it Home Assistant (or HA in short). For me hassio is Home Assistant, so in that regard your logic has merit. You want the mainstream user to use hassio (better said Home Assistant).
For new users this naming scheme is a no-brainer I think, but I understand that the community that already use HA in one way or another can find this confusing. The thing is (and was the reason I commented about this in the first place) the forums are full of questions about the differences between HA and Hassio and they will remain there for quite some time. I often find some information that I think is useful only to find out it no longer works or is outdated. (this is not a problem btw, it’s just how forums work in general). I do however think it might pose problems for new users not understanding why people talk about hassio.
But again, admittedly with your explanation it does make sense.