No it's not. Actively managed funds will in most cases not beat an index fund. Investorers have learned this and has chosen passive funds. This together with more people investing in funds has increased the size of passive ETFs in the market.

They don't beat index funds because their fees eat their gains

They don't beat index funds because the market is completely unpredictable, and active investors are just delusional and think they can predict it. They can't.

Do you have proof of this over long time horizons? Say 10 or 20 years.

And the odds of picking the right managed etf over index fund?

Usually those active managers stay in business by saying they get "superior risk-adjusted returns" even though they didn't outright get better returns.

This is, of course, changing the goal post because a portfolio with 90% S&P 500 and 10% cash will also appear "superior risk-adjusted" than 100% S&P 500. Sharpe ratio is the most misunderstood metric invented by humanity.