I guess all I'm saying is that a strategy that has a worse Sharpe ratio than the market but zero correlation could still be valuable to a lot of investors for the same reason that sometimes it makes sense to add a asset to your portfolio that lowers your expected return. It's possible that that one strategy with the worse Sharpe ratio when combined with your pure beta investments would yield a portfolio with a better Sharpe ratio than either allocation alone.
Apologies if I misinterpreted your comment, just my thoughts when reading it.