My biggest issue with hypercarries in League is the way in which their power curve is implemented. Personally, I do think a player should be able to enter godmode and solo carry a game, but only if they work appropriately hard for it. If a champion starts off at a severe disadvantage, is forced to put themselves in risky and difficult situations versus enemy champions to progress, and succeeds, then imo they deserve to come out of that with a significant boost to their power. Kayn is a good example of this, even though he's not a hypercarry, because his powerful transformations only occur once he participates enough in combat while in a less powerful state.
However, hypercarries in League typically spike with gold, which they mostly collect by farming safely, and as such that typically leads to a degree of very boring and uninteractive gameplay, and an increased amount of frustration for the opposing team, who ends up feeling like they couldn't do much to prevent that time bomb from going off. This is why Feral Flare was a balance nightmare that felt like shit to play against, as well. Effectively, hypercarries should have their power awarded for completing difficult objectives that force interaction with their opponents at an appropriate disadvantage, yet champs currently hyperscale in a manner that is neither particularly interesting nor interactive.
Another problem I have with hypercarries is that their power tends to overwhelmingly influence their combat effectiveness: personally, I'm perfectly fine with having effects that put a team on a clock, so long as that doesn't limit interaction between players. Heroes of the Storm has a character named Sergeant Hammer, for example, who can fire the equivalent of an Ezreal ult, and who can upgrade it at later levels to cycle the map non-stop. Because most abilities damage structures in that game, this means she can position her ult to repeatedly pass through structures from global range, putting the enemy team on a clock where their structures will inevitably all be destroyed, given enough time. However, because this doesn't really affect her power in combat, it does not limit her counterplay. Hypercarries in League could learn from this model, and I'd be interested in seeing hypercarries defined by their ability to reliably push towards the enemy nexus, without that power translating to overwhelming dominance in fights. When a champion begins to auto-win fights simply because someone decided they should scale that way, that's not really fun for anyone involved, not even for the hypercarry player who suddenly finds themselves without any real challenge.
Finally, one issue I take with League, and to a lesser extent DotA/Dota 2, is that those games still overwhelmingly rely on a model where each team is centered around a carry. If your team doesn't have a carry and the other team does, when skill levels are equal you're practically guaranteed to lose no matter what, and that I think ends up removing depth to team compositional choice, and reducing diversity overall in match dynamics and diversity. Additionally, this tends to lead to unsavory dynamics where other players have to babysit the carry to cover up their early game weakness, which in the end removes a degree of risk that is supposed to be essential to that carry's gameplay and counterplay. On top of that, it leads to the feeling mentioned in the OP, where at the end there's only one star to the show in every match, and everyone else just automatically turns into a secondary character. While this may be an interesting dynamic to have in some matches, particularly if one particular player carries their team through good play, rather than through arbitrarily assigned scalings, I don't think this should be the universal model to all gameplay in League, as I think every player deserves to shine individually and have an equal amount of agency.
TL;DR: Hypercarries should scale through risk and exceptionally good play, not by safely farming gold; we need hypercarries to remain interactive in combat at all stages of the game, and so more hypercarries whose power gains translate into objectives rather than fighting; League needs to stop making every match revolve around a carry champion, and should allow games to work perfectly fine with exactly zero carries on a team, or at least with comps in which every player has about equal amounts of agency and presence.
and ADC 
?
Her kit, by itself, is adaptable to the extreme, able to swap from massive burst to incredible sustain. Everything she does increases her ability to chase or kite, and it does so in an anime-like superhero fashion. If you are low, you die as a punishment.