I'm only through the introduction right now, but assuming that it's representative of what's coming later, Piketty isn't saying 'r > g' as mathematical fact, he's saying 'when r > g, divergence in the distribution of wealth happens' and 'empirically r has frequently been and is again moving towards > g'. And his concern with this is the same as the problem you state, that r > g implies, eventually, r = g, which translated back to English means economic activity devolves into rent paying.

Quoting:

"When the rate of return on capital significantly exceeds the growth rate of the economy (as it did through much of history until the nineteenth century and as is likely to be the case again in the twenty-first century), then it logically follows that inherited wealth grows faster than output and income... Under such conditions, it is almost inevitable that inherited wealth will dominate wealth amassed from a lifetime's labor"

"Forces of convergence also exist, and in certain countries at certain times, these may prevail, but the forces of divergence can at any point regain the upper hand, as seems to be happening now, at the beginning of the twenty-first century"

"My conclusions are less apocalyptic than those implied by Marx's principle of infinite accumulation and perpetual divergence... In the model I propose, divergence is not perpetual and is only one of several possible future directions for the distribution of wealth"