It is like, imagine if USA had written in the constitution that the rich should get richer? Would you defend that move by saying "Well, the rich gets better investments anyway so this wont make a difference!".
It is a "fundamental law" in both PoW and PoS that you get rewarded for doing the work/staking. I don't really understand your point about the US constitution -- what I am saying is that PoS systems minimize the effect of the "rich getting richer" as much as possible by forcing it to be at most a linear effect. Whereas there is no need to include such language in the US constitution at all.
If I invest in Bitcoin and its price increased by 10%, I did not lose money if it turned out that real estate would have gained by 20%. I still gained 10%. Actually, only if I sold it.
That's not "losing money", it's not maximizing returns.
Further, you're still missing the double effect of staking. With staking your portfolio value will depend on the price of the token, yet since you staked it (it's locked up), it's a paper win/loss. Further, regardless of that, you get NEW coins for free.
Further, it's not linear at all. It's whatever the token does, which can be linear, parabolic, anything.
You are right that you wouldn't normally consider alternate investments like that. But with PoS, where the only cost is the time value of the money staked, it is the only thing to compare.
If you reason like that, I suppose in your world fireworks is the same thing as a rocket bringing us to Mars?
Is running Amazon and making a profit the same thing as just milking interest from a bank account?
These differences aren't trivial, they are massive. In a PoW world, most rich people don't mine, they just hold the crypto. In a PoS world, said rich people auto-mine by just holding crypto.
No, what I am really saying is that PoW mining and PoS staking aren't so dramatically different in complexity like you are saying. They are actually both complicated businesses with variable yields. The only difference is that with PoW, the benchmark is electricity cost, whereas with PoS the benchmark is the other investments which you could have invested your staking money into.
When’s the last time a billion dollar staking operation had to build multiple mining datacenters and fill them with hundreds of millions of dollars worth of hardware? That’s just not required for staking. It just isn’t. They’re not equivalent operations. Not in any way. Not by any stretch of the imagination.
Which of these two scenarios seems to favour the rich, in your mind?
I would say it’s harder to compete with miners than stakers.
There’s really no comparison. Running a business with high fixed and variable costs, and considerable competition is far more difficult to pull off successfully than a passive investment. Which one do you think favours a “gilded elite” more?
Putting money in a bank isn't even enough to keep up with inflation at the moment, the same is true for Proof of Stake coins, too.
With PoS, you do nothing except maintain your staking hardware and burn the time value of the money you are staking.
From that perspective there is no difference. The difference is that with PoW, the richest participants can afford the most efficient hardware, giving them a super-linear advantage. In PoS, it's still true that the "rich get richer", but only at a linear rate, since there is no way to improve the efficiency of staking (which is basically the best you could ask for).