High movespeed still lets you dodge skillshots, still lets you chase champions easier, still lets you escape easier. What the heck else do you want from mobility anyways? If extreme movespeed does exactly everything mobility does, then why would you NOT call it mobility?
Yes, I would consider Soraka's passive mobility, as it's quite a strong burst of movespeed, but she's not really 'a mobile champion' - it's quite limited in scope. No, I wouldn't consider Cassiopeia mobility as much, because it's not as extreme a boost as the other two. Yes, I would consider Zilean able to make anyone mobile for a short time. No, I do not think there is a black-and-white line between when movespeed becomes strong enough to call it true mobility; it's a rather grey area that's best taken case by case. I would not consider Teleport a mobility summoner, even though by the technical definition of "instant dash/blink" it is, but I would consider Ghost a mobility spell, and I think you'd be crazy not to.