Not only are these not assumptions, they're trivially proven with even the briefest of research on the subject. Capital hoarding: go look at GDP graphed against wages over the last 60 years. Wages don't go up, so all that extra productivity is going in -someone's- pocket. Capital hoarding is destroying modern society: global news media is largely controlled by 7 organizations, the international housing market has been invaded by investment funds, healthcare outcomes in the US continue to lag behind most industrialized nations worldwide despite record profits, the list goes on. It has never been harder to get a leg up (at least in the US) at any point in the last 50 years, and the percentage of US households that are living paycheck to paycheck keeps increasing year over year. Not sure what you're stanning over there but that is definitely an impressive set of blinders you've got on.
Capital hoarding only refers to wealth being held back from the market. Investments wouldn't count because you are lending your money to others and that generates economic growth. I think you are conflating terms with some other inequality concepts.
You're clearly trying to shorthand a lot of disparate political topics into one point (a good share of hospitals and insurance companies in the US are non-profit - it clearly doesn't affect medical prices), but I don't think it's as clear cut an issue as you are making it.
I mean if you want to pretend the issue is murky despite one being able to toss (at random) a loose collection of off-the-cuff examples so be it, but I don't think your confusion is rooted in much beyond cognitive dissonance. Put even more simply: the haves are taking too much from folks that actually work, hampering their social and economic mobility.
I'm not trying to argue against inequality or even a wealth tax.
But France is in a demographic collapse the likes of which has never been seen before in the country. There simply not going to be enough working age adults to supply all of the goods and services the dependents of the state are going to need. Furthermore, major international trading partners are a) increasingly cutting them out of trade deals and b) waging wars amongst each other.
So while I think inequality is certainly something to deal with, it is not the sole boogeyman. The idea that wealth is just some sort of economic piggy-bank that can be raided for easy gains is vaporware.
