I hadn't heard of the Lucas Critique before, but it seems to be constrained to policy advice that operates on economic variables over which market actors have control, and I'm not sure that applies here - I'll have to think some more.
> Not sure I can explain better than the comment I linked to. ...
Thanks for the clarification, I'm not feeling very switched on at the moment. I would question your analysis though. It is certainly correct on its own terms, however it conflates wealth with capital (which is something I've seen people saying Piketty does - does he?). To me it seems to be vital to include both major sources of income, capital and labour. If you do that, then you can calculate the quantity
(Xl exp(gt) + Xc exp(rt)) / ((Xl + Yl) exp(gt) + (Xc + Yc) exp(rt))
Where Xl and Yl are the labour "holding" for X and Y, and Xc and Yc are the capital holding. Here I'm taking r as the return on capital, and g as the return on labour, which seems abusive but I think it captures the point. This quantity tends to the capital ratio where r > g, and the labour ratio where r < g. Whilst it ends up at the same limit as your model (for r > g), it shows that there is a shift of wealth from labour to capital over time, so the inequality between capital holders and labour "holders" increases over time, as the returns on labour are dominated by the returns on capital.
edit: Just thinking about it a bit more, this implies that we definitely do want g > r, because then in the limit wealth is proportional to labour, i.e. productivity, not to capital bequeathment. One can still make returns on capital, but in the limit your wealth will be proportional to your effort. Surely that is the goal of a meritocratic society?
edit edit: To clarify, I have broader views on the value of pure meritocracy, in my first edit I was just trying to relate the implications of the wealth ratio given above to meritocratic goals.