I remember the week after Kai'Sa's release, where a great deal many players went to the Boards to warn Riot not to overbuff her, as they did with every previous release that started out with a low win rate. We brought up many past examples of champions suffering, including many who suffered much harder (e.g. Ivern, Tahm Kench, Gnar), before turning into complete balance monstrosities after a few misguided buffs, in addition to dominating the competitive scene the moment pro players figured them out. Riot's response to this was to reassure us that this time would be different, that these buffs were extensively researched and tested, and that they were sure to land Kai'Sa in just the right spot. They didn't. This total lack of hindsight worries me, because not only does it indicate that the devs balancing new champions aren't learning from past mistakes, but it also suggests that they refuse to learn, and somehow believe that repeating the exact same methodology as before will somehow produce different results.
I absolutely agree with the OP here: one week, let alone a couple of days, is not a good enough window of time to properly assess a new champion's strength. There is always a learning curve, especially when Riot releases more complex or mechanically difficult champions, and it's only once a certain number of players have gone past that curve that we can have a better idea of where a champion lies in terms of power. What Riot is doing right now is that they're effectively balancing new releases around their win rate at under 15 games, which as anyone can check on any stat site, is always much lower than a champion's actual win rate over a larger spread. This effect is even more intense on new champions, because players are figuring their kit out on their own, and do not yet have any sort of solid build or guide to follow. Because of this, I think we need at the very least one patch cycle to gauge a champion's power: if they're doing far too well, then for sure they could get hotfixed, and the same should likely be done if they have some crazy low win rate, e.g. some sub-40 win rate as was the case for Syndra and Azir (though both happened also because the champions were super buggy on release), but anything in-between should be met with patience and proper analysis.