The important difference is that all of this acquisition is a result of tens of thousands of years of consistent natural selection. It's hard-wired because humans have needed these things, and children have needed them as fast as possible, for a long long time.
The things humans attempt to learn in modern times however (non-native languages, formal systems of logic, the ability to argue and reason in complex fashions, the ability to program complex systems) are completely evolutionarily unprecedented, and the result is clear: children are not able to acquire these behaviours effortlessly. They don't just rub off. Instead they (generally) require focussed, extensive supervision and tuition from humans that have already put in the hard work of mastering them.
So the relevance of neuroplasticity still seems small to me.
At least in the case of non-native languages, while it may not be "effortless", every study I've seen has indicated that it is much easier for children to learn them.
And now that I am older (mid-20s) and my brain is supposedly less plastic, but I have motivation, context and determination in abundance, I feel like I am really learning and developing for the first time in my life.