Your conclusions are very surprising as there has been a lot of other academic research which reach very different conclusions.

Surely you know about Eugene Fama and Kenneth French's 1992 study in which they put virtually all U.S. stocks into beta deciles for the period 1963-1990. Per Burton Malkiel's book, A Random Walk Down Wall Street, "The remarkable result,..., is that there was essentially no relationship between the return of these decile portfolios and their beta measures." Other studies have reached similar conclusions as regards other non-US markets.

Hence, the (relatively) recent introduction of minimum volatility equity portfolios - which are also low beta. ("Recent" relative performance has been subpar, though, in line with your past decade results.)