Maybe too harsh. But I've known many cases of toddlers dying in which parents left them alone "just a second": jumping through windows, drowned in the bathtub, etc.

What children want is doing (specially discovering and learning) things by themselves, but that's not the same as being alone.

And every child I've seen wants more attention from their parents. There's an age for everything and that's not the one for unsupervised independence.