Lots of people think they can beat the market for lots of different reasons. You think you've thought of a reason. Here's how your hypothesis can go from spotting a market inefficiency to creating an investment strategy and your own active fund, to the result that a low cost index fund is still the most advantageous long term investment for most people.
Most importantly, I think you'd (or some savvy market participant, feel free to substitute all instances of "you" throughout this answer for "savvy market participant") have to do some backtesting to test your hypothesis to determine what if any effect there is on a company's stock as a result of being added to or dropping out of an index. I know there are answers related to the efficiency of the market and if an opportunity existed some number of people are exploiting it to the point that you can't see it. I doubt there is an inherent measurable effect here. Just because a market effect seems logical doesn't mean the phenomenon presents itself predictably in the market.
If you can predict what an index fund has to do can you profit from that movement? Maybe. If a company is falling out of a large-cap fund to a mid-cap fund because of bad news maybe by the time the funds have been forced to transact the company's stock has already been reduced to the point that other traders are interested in buying? There are literally incalculable numbers of forces and opinions being applied to securities transactions, I'm not sure any are anymore reliably predictable than any others.
Say you back test your hypothesis that you can regularly profit from constituent movements in and out of various index funds. You roll up a fund, and hire people, pay for your space, buy your access to the markets and have your own transaction fees. For all this work you charge a measly 1% to all your investors. Now you have yourself an actively managed fund, of which there are thousands. Your fund, and all other actively managed funds with similarly great ideas to profit in the market, and all other active market participants set the prices of securities, there was bad news, sell; you think the news wasn't that bad and the company is a buying opportunity, buy. This company has these new opportunities, buy; those new opportunities are overvalued, sell. And on and on. In a given year all of this active trading work roughly translates to the average result of the market. Some years a lot of these active funds will outperform the market, some years those same funds won't. The law of averages and regression to the mean, sort of dictate that on a long time line your Big Bad Active Fund will do about as well as the market did. But you're charging 1% for access to Big Bad Active Fund, and I can just go get VOO which will return the market average and only cost 0.03%. So even if your fund can manage to return the market average I'll lose 0.97% of my account every year. For me to stay flat, your fund has to beat the market return by at least 0.97% every single year. Sure, you'll have years where you earn double and even triple the market return, but regression to the mean shows that your extraordinary gains will come back to the average over time.
Jack Bogle, Warren Buffet, and a number of investing gurus (for lack of a better word) advise most people to simply allocate their stock market risk to a low cost broad market index and go about their life. Don't bother paying the active managers for their research and offices, just buy the market average return for 97% less cost to you. They say it's because the active managers can't beat the market, really it's simply that they have to charge too much more than the big broad market index funds that don't need research and analysis teams.
But we will never run out of individual investors because someone needs to control the boards of directors and we will never run out of active funds because there will always be optimists who think they can beat the market.