IT would not work. Not poorly, it just wouldn't work at all. This tells me that there is a balance on how much active/passive investment can there be, and at some point they will be balance by some criteria.
If the population grows 3%, we have to produce roughly 3% more, so revenues go up roughly 3%, number of employed goes up roughly 3%, so the economy grows 3%.
If I invent a steel manufacturing process that makes steel 3% cheaper, expenses go down 3%, profits go up, supply goes up, prices go down, the economy grows.
If all you do is passively invest, then over large periods of time you should on average see returns of, roughly, population growth + innovation. Even if everyone is passively investing, it's the same thing. If you actively invest, but still invest in the whole market (as any diversified investor does), you get the same thing, minus ~1% towards. If everyone was actively investing before, and the market grew ~8% per year, and now they passively invested, why would the market not gain the same?
Plus, it's not like passive investing causes securities to never be traded, when I buy into a mutual fund I'm buying stock from someone. That someone is probably retiring and selling their securities.
Lastly, most "active traders" just buy a bunch of Blackrock/Vanguard/SPDR index funds anyway and call it a diversified portfolio that only they could deliver.
Passive investing works thanks to active investing. Funny huh?