Earlier quoted context omitted.
Nelson doesn't lament that his mind wasn't adequately "cultivated" but that he wasn't taught some basic skills that he quickly, but probably painfully, acquired on the job and which presumably he found critical in his career. This isn't a question of "mental development" but of having useful things pointed out so that you don't have to suffer whatever damage accrues from not knowing them.
I suppose we're splitting hairs here about what he's aiming for, but consider his comments, first, about what he learned on the job: >"My first six months, what did the consulting firm teach me? They didn't teach me the basics of how they do business. They taught me how to think. I didn't know how to check my work. I didn't think about order of magnitude. and then his goals for Minerva: >"We want to teach you how to…
> I didn't know how to check my work. I didn't think about order of magnitude.
I suspect in these cases he learned some useful trick or mode of thinking in a matter of minutes by having someone point it out to him. Not so much "basic" as "simple".
And irrespective of whatever Minerva claims to do I think it is clear that many "elite" graduates feel there are simple, useful things not being taught in schools which ought to be.