I see parallels too, but trickle down economics is about sending capital "up" in the hope that what's produced trickles back down from wealthy people, whereas the idea of investing in lots of people is more like sending capital "down", or at least sideways.
I think a plausible factor in the failures of trickle down economics to enrich the masses as much as hoped by those who advocate it, is wealthy groups of people acting so as to keep what wealth they have in their own control, away from others. And, over generations, perhaps ceasing to be wealth generators (e.g. inventors and industrialists) and becoming wealth controllers (e.g. "old money" families).
Widespread investing in lots of people isn't subject to the same problem, by definition. (Assuming those people are paid decently, rather than indentured servants to some capital controller).
The minute you give a bunch of people $1-3MM as upthread (https://qqrl.tk/item?id=21034871), you're sending $30-90BB "up", by definition, from the perspective of the typical American (median household wealth of $97,300). It's perhaps just not as far up, so not as far that it needs to trickle down, but it seems more or less the same on a zoomed out level and puts the recipients at 10-30x the median wealth. Simply investing that sum in index equity funds would typically provide a income to place a household around the median household income over a four decade period without working.
Maybe trickle down actually works. Maybe we all got a return on it in invisible ways. Maybe things would be a lot worse for the median taxpayer than they are after the policy was enacted. How would we know for sure?