No, haters still cling to the idea. Does not make them correct though.
The Switch was made for adults first, as the ads show. It has IPs like DOOM, Octopath Traveler, Wolfenstein, LA Noir, Skyrim, Disgaea, Xenoblade, Outlast 1 and 2, Diablo, etc on it now. None of these are geared toward kids.
They continued investing in Bayonetta and brought back Prime. Even games with artistic styled graphics such as BotW are catered to adults gameplay wise, as kids get lost in such deep open worlds. Games like Splatoon 2 appeal to both, and are neither kiddy nor adult.
So no, the Switch is not made for kids, nor does it look like it is. However this is the internet and haters will cling to whatever they can to downplay, especially when what they are hating on is successful. False as it may be, the idea will never die.
Splatoon appeals to both because it's geared towards teens, so it ends up reaching them, as well as younger kids that want to be cool like their older siblings, and adults that are still kids at heart but just can't do the complete E for Everyone child friendly aesthetic. I'd argue that marketing for Zelda has shifted to teens as well, but with a less edgy aesthetic, using depth of gameplay to make the appeal instead, as you said.
I think that while there always may be some haters, eventually if Nintendo keeps at their current marketing and branding, and keeps making games with adult appeal, the kiddie label just won't stick, and the insult will ring really hollow, and eventually we just won't hear it as much. It may take through all of Switch's and its successor's lifetime to really acomplish this though. If Nintendo courts a generation of younger gamers with its titles with more kiddie appeal, but gives them plenty to want to move onto that feel less kiddie for when they want to feel older, and plenty of adult content for when they go through the phase where they lash out at kiddie things so they don't get made fun of in high school, eventually you'll have a whole generations of gamers that never felt the need to go to Sony or Xbox to avoid looking childish in front of their friends, and the insults won't even make sense anymore, because they could point to Nintendo games they play that aren't childish, and point to Sony's and Xbox's attempts to appeal to kids and say "so if I'm kiddie because Nintendo has Mario/Yoshi/Kirby, why aren't you kiddie because Xbox has Lucky's Tale/Kinectimals/Ori or Sony has Knack/LittleBigPlanet/Tearaway?" And eventually even the haters will feel like it doesn't really work as an insult and shut up.