They’re the smarter place for people to put their money but I wouldn’t consider them a comparable product.
Additionally, your description of how people purchase and make money on indexes funds is incomplete at best. Really, it's just factually incorrect in that it presumes a certain purchase strategy. People do short-term, dopamine-inducing trades of index funds all the time.
But, I don't think elected representatives should be able to do that, either. At the very least, successful short term trading - directly or through an advisor, of an individual security or a fund - creates the appearance of impropriety.
If congress has to bet on the overall economy instead of e.g. spotting that riot gear providers goes up when country goes down, that would be a good thing?