I recall my peers would often ridicule Nintendo games for being "childish" compared to most of the games that were popular in the post-9/11 era, so I take it as a compliment from them that I was a fan of "childish" games.
Indeed. There are a few reasons for that. In the early to mid 90's, Nintendo and Sega's marketing focused on different age demographics. If you look at Sonic, you'll notice his shoes and "attitude" that catered to the adolescent "hip" crowd.
Nintendo's biggest blunder was to censor the blood in the SNES port of Mortal Kombat to please members of Congress. Like the game or not, Mortal Kombat was definitely a counter culture game at the time.
The other reasons for Nintendo's "kiddie" image are more benign: No first person shooters, more colorful palette, the "purple lunchbox" GameCube, just a lack of graphic violence in general.
I feel like most of these moves by Nintendo were not done to please the kids but to please the adult parents. They didn't have to make violent games themselves, but they could have allowed other developers to publish violent games on their platform.
Here is an example I found of what you are referring to:
https://youtube.com/watch?v=uEYS0CmgJL4