As the W/Ynet ratio rises the net rate of profit is likely to fall, and so it is highly unreasonable to imagine that the net savings rate out of income snet will not fall rapidly and substantially and so greatly attenuate any rise in W/Ynet. Thus substantially rising W/Y is not a problem that we should expect to see.
Should the W/Ynet ratio rise substantially, the net rate of profit is likely to fall, and so the share of income earned from wealth will rise only slightly--and may not rise at all. This is not a problem: this is wealthholders providing workers with lots of capital services at a cut-rate price. Thus rising W/Y is likely to rather than lowers working-class incomes and is unlikely to worsen the income distribution, and so the prospect is not a problem.
Even should the W/Ynet ratio rise substantially and even should the net rate of profit not fall, wealth is unlikely to become or remain highly concentrated. A high W/Y and a high r x W/Y is a big problem only if wealth becomes and remains highly concentrated, and that we are unlikely to see.
Even should the W/Ynet ratio rise substantially and even should the net rate of profit not fall and even should wealth become and remain highly concentrated, plutocrats are highly likely to get into status games of spend-my-money-to-change-the-world, and so we are unlikely not have a world in which heirs and heiresses exercise undo influence over our priorities. Even should the distribution of wealth and of income become markedly more unequal, it is unlikely to distort society's choices and lead to a grossly unequal distribution of utility. READ MOAR:
I figure each of these has about a 20% chance of coming true, and thus that Piketty's scenario is a (slightly) less than 50-50 shot, even with policy and politics on autopilot. Of these, I think (2) is the most important: why should we care if W/Ynet rises if r x W/Ynet Does not?
And, of course, there are also a bunch of issues on the other side--a bunch of questions I have never in 35 years gotten answers to concerning why we take the Solow model as the baseline:
Why is depreciation a "rusting" constant fraction of capital value, rather than proportional to D utilization or related to obsolescence and technological progress?
Why should gross savings ever be a constant fraction of gross output? What possible rule of thumb in a world in which people receive their net incomes could possibly generate such an outcome?
Plus there is the… rather odd… Handling of population growth vis-à-vis per capita income growth in the Ramsey model...
A significantly better baseline, I think, would have net investment as some parameter times next income from wealth plus some parameters times net income from labor, and have the rate of net profit as some reasonable function of the wealth to that income ratio...