Except under mining, increased investment opens up access to better equipment like ASICs, access to cheaper energy agreements, etc. But no amount of $ unlocks the ability to validate faster (per unit staked).
To clarify: I don't think proof of stake is perfect.
I think the original pie in the sky dream, as hinted at in the Bitcoin white paper, was for decentralization through anyone (all the way to students in their dorms) being able to participate in consensus.
I don't think proof of stake gets things all the way there, but I think it does get closer to a linear ROI curve, compared to how proof of work is right now.