Op.gg updates every few days to include items that are recommended by the percent of players using it (win rate is not accountable unless you select the option to show items based on win rate). The same may apply to builds on champions, which could recommend items based on popularity based on the lane the champion is being played in. The game already changes up builds depending on where I play a champion, such as if I want to play Brand: I'll be recommended different items that accommodate each role. The problem with this is that the most effective items for said champion are >>usually<< different from the ones the in-game shop recommends.
As an example, Twitch Jungle vs. ADC possesses some differences between the build recommended between the two, thought it is only a minor variation. Regardless, the system takes into account the lane the champion was selected in, similar to how it already functions in the client. I will say I have found issues with the site in general; sometimes updated builds for champions will only show in the items category of the champion page, rather than on the overview for some odd reason.
In regards to builds changing, I can understand the point you're making there. My only argument would be - using your Neeko example - the builds that are changed are usually better than the ones that were previously used. As confusing as it may seem for new players, I'd opt to have the new player adjust to better builds they aren't used to than use crappy ones that they are. The reason for recommending the most popular build is to allow for new players to maximize the potential of the champion rather than building items that aren't nearly as effective as the ones that are being utilized.
My frustrations stem from me identifying someone on my team building their champion wrong, and then telling me "they're building from the recommended build" that they have in item shop. Obviously if I could take the time to refine my suggestion a bit more, I would, but this thread isn't really gaining traction... So IDK.
TL;DR: Riot has the data to be changing builds based on popularity, and it would keep new players from relying on incorrect builds from item shop's recommended section.
But yeah - just an idea I was throwing out there.