The Human Development Index: undermined by its own success?

So says Lant Pritchett:

The Human Development Index (HDI) has been a politically and rhetorically powerful counter-point to measures of “development” that focus exclusively on economic indicators, such as Gross Domestic Product per capita or household consumption expenditures. However, the relevance of the HDI is increasingly challenged by success.

For instance, by pitching the education component of the HDI at a very low level (literacy and gross enrollment) which has an upper bound, as more and more countries attain near 100 percent literacy and 100 percent gross enrollment of the young the education component ceases to contribute to progress in the HDI.

For countries above the low educational thresholds this implies that more progress in education (e.g. expanding tertiary enrollment, improving quality of learning outcomes in primary school) does not raise the HDI while increases in GDP per capita do raise the HDI.