It's definitely slowly improving, but a walk through the toy section of my store has still saddened me on occasion. And I live somewhere that would be globally considered generally "socially progressive".

but I’m hoping that the more chaotic distribution weakens the willingness to internalize stereotypes

It will, but it's also going to be pretty obvious to them after a while that the girls at school always play dress-ups with dolls at lunchtime while the boys are playing with toy cars and trucks. Kids start really getting the hang of categories, associations and social cues with language development from around age 3 and up.

They especially will notice when one kid (or worse, adult) says "you can't play with that/them, that's for !" Or "I'm not going to do , that's for \s!". Then they have to try to figure out what makes their family so different and why they aren't like others, which can lead to some interesting hypotheses as a young child.

I vividly remember some boys objecting to singing in class at school when I was very young (6?) because singing was for girls. The teacher asked them what they thought about the most famous male singer of the time, and they uncomfortably shuffled around and grumbled as a response. It was clearly conflicting information for them, and I think it might have been the first time I encountered someone openly challenging gender expectations.