Yes, but then why invest in an actively managed fund at all, as an LP? whole premise is that fund managers can beat an index such as the S&P500 or total market etc.
For large institutional LP's like pension funds, endowments, charities, etc, they need steady smooth returns that they can draw upon year after year to fund their beneficiaries. In particular a down year really hurts them since they will have to draw down on their principal. This is a very different risk calculus to an individual saving for retirement who can stomach 30-40 years of stock market volatility with a good probability of having enough money at the end of their career.
So rather than chucking the bulk of their fund in to the asset with the highest expected returns as an individual might, these institutional investors buy a big basket of very different return streams (i.e. as uncorrelated as possible) to smooth out the bumps in each one.
That's why diversification is important