Your idea is wrong for various reasons.
1. You equate being an alpha with merely being physically fit - that could be valid in 4,000 bc but not now.
2. What you mention here about small number of alphas would be ok if two things were true a) that mate guarding is allowed in modern society b) alphas are extremely stupid and don't think about contraception.
But both of these are false, so alphas are actually less successful than ACTUAL OMEGAS, who are men who use seduction. Omegas like Roosh are more successful than alphas like Sergei Brin.
3. Men can advance science and technology better when they're married. The free time idea is idiotic. Loneliness inflicts suffering.