I don't think it has really destroyed the kiddie image.
It has changed a lot but it still hasn't made it a thing of the past.
What i think it remains is the type of games that Nintendo is bringing to their consoles.
It's one thing to have 3rd parties put out some old/oldish ports, another is seeing the big games arrive on the console and seeing Nintendo change the type of genres they make.
So far, the biggest titles still elude Switch and Nintendo's own repertoire hasn't really changed.
In my opinion, the most important and hardest thing that needs to happen, is for Nintendo to start developing their own Halos, GT, Destiny, Uncharteds, etc., etc.
Over the years Nintendo has tried to change demographics and show that they aren't just for kids, but at the end of the day, their own image (SW production) did not change. And you can have great marketing, great consoles, but if you can't serve as an exemple of said change...