Yes, if this was a very high volatility bet with a low payout that can't be easily repeated it might not be arbitraged away efficiently.
But this should let you make predictions about literally every single company in the world if it's true. You can take it thousands of times, not once per year. So I don't think the situation you're positing applies here.
If CEO salary was a signal as to equity performance, you could make a "CEO salary weighted S&P index" that should outperform the S&P consistently. Which we don't observe. Therefore it probably isn't a signal. Or if it is a signal, it's very weak.
In short, you're saying that by diversifying your holdings across thousands of companies, you can statistically arbitrage the signal but it is not true.
You could make predictions for every company in the world but you'd need both the signal to be right most of time, over any time period, be uncorrelated across companies and have an excess return collectable over a period short enough.
If any of these conditions are not met, you will not be able to statistically arbitrage it.
Take options for example, writing them (selling them) is a strategy you can backtest and it has positive return on average. You can write options on thousand of stocks, every week. But because volatility - on which the option price depends - is correlated across stocks, this strategy will incur a large loss on a financial crisis. Your diversification will not matter.
Also, you say that we don't observe the signal but you can't know, maybe we do. There are tons of simpler signals - some of which I cited above - that we still observe.
But this should let you make predictions about literally every single company in the world if it's true. You can take it thousands of times, not once per year. So I don't think the situation you're positing applies here.
If CEO salary was a signal as to equity performance, you could make a "CEO salary weighted S&P index" that should outperform the S&P consistently. Which we don't observe. Therefore it probably isn't a signal. Or if it is a signal, it's very weak.