The wealth distribution of bitcoin is even worse than the wealth distribution of society as a whole. Further, I suspect that this would be the typical state for any finite/limited asset. IMO, things like bitcoin (and gold) as a primary wealth store are how you create stratified societies with entrenched elites and banking orgs with more money/power than nation states. Not that bitcoin could ever happen dominate, but it's certainly not egalitarian in any sense.
I would expect it to get worse, over time, too. When the block reward was high, it meant that the (strictly financial) cost of actually operating the Bitcoin network was covered by Bitcoin dilution, which meant that everyone was paying it pro rata based on how much Bitcoin they actually own. As the block reward decreases, though, it increasingly has to be covered by transaction costs. That's going to progressively price people out of participation in the direct Bitcoin economy.
I can see using Bitcoin as a primary wealth store, similar to gold. I agree, it would have most the same social features, which seems problematic since none of that is really in line with Bitcoin's original political vision, but I'm not sure Bitcoin's original political vision is anything more than a piece of nostalgia cherished by people sitting on the periphery of the contemporary Bitcoin economy, anyway, so maybe that's no big deal.
The bigger problem I see with Bitcoin relative to something like gold is that it has some troubling practicalities. It's theoretically much easier to steal vast sums of Bitcoin in one go (because 1,000,000 BTC wouldn't be quite as subject to conservation of momentum as a tonne of gold bars would be), and it's definitely much easier for vast sums of Bitcoin to accidentally poof off into a crypotgraphic pocket universe where nobody can reach it anymore.
One that has a fixed block subsidy. After any amount of time, whether years or decades or centuries, it will have been distributed evenly over all that time.
Rather than having 50% distributed in just the first 4 years, and only crumbs in later decades.
I don't see how that logic follows, if this was a fixed block subsidy over the first 4 years instead of just 50%, surely the situation you are describing would be worse ?
There's a huge difference between fixed forever and fixed for only 4 years and then dropping to 0. Bitcoin is closer to the latter (instead of dropping to 0, it keeps halving every 4 years). Gold is closer to the former.
"Egalitarian currency" and "store of value" are somewhat mutually opposed goals.
A stable store of value is always going to socially/psychologically encourage hoarding and other human traits that lead exactly back to inequal distributions of value ("wealth").
A truly egalitarian currency would need to focus on the velocity and acceleration (the current of the currency) curves far more than the value at rest, which likely would be an afterthought.
