Conjecture that most finite groups are nilpotent

Statement
For any natural number $$n$$, define $$g(n)$$ as the number of fact about::finite groups whose order is at most $$n$$, and let $$g_{nil}(n)$$ be the number of fact about::finite nilpotent groups whose order is at most $$n$$. The conjecture is that:

$$\lim_{n \to \infty} \frac{g_{nil}(n)}{g(n)} = 1$$

Related facts

 * Higman-Sims asymptotic formula on number of groups of prime power order
 * Pyber's theorem on logarithmic quotient of number of nilpotent groups to number of groups approaching unity