You need a name for things. And long flu might have different etiology than long covid despite similar symptoms, so it doesn't make sense to lump them together as "long virus".
I think there's precedent for such a decision in how concussions are generally viewed. An individual can be diagnosed with a concussion, which has common, acute symptoms. If the acute symptoms last longer than is typical for a concussion of a given severity, the individual could be diagnosed with persistent post-concussive symptoms (a.k.a. post-concussion syndrome). Of course brain injuries are different than viral infections, and we still have a ton to learn about brain injuries, but it's the idea of clearly differentiating between the acute effects and the chronic, persistent long-term effects.
To be clear, I'm not trying to relate COVID with concussions beyond the medical nomenclature, but I think the nomenclature is effective in making the distinction to which I'm referring. It's not perfect, but we'll never have perfection in research.
Edit: It's unclear if the paragraph breaks are displaying properly, so I apologize if it appears as a wall of text.
Isn't that akin to "long covid"? No one mistakes post-concussion syndrome for a concussion, and no one mistakes long covid for an acute infection.
We do have a formal name for long covid: PASC (Post-Acute-Sequaelae of Covid)
It won't catch on a regular name because it's unpronounceable, but it there for the scientific literature and those who wish to speak formally.
I'm open to there being a better way, but ultimately you need something people can refer to, as it is a common phenomenon.