A necessary ingredient? In this bald form, this is a very dubious argument -- a neo-Malthusian theory of development: getting rid of 'surplus' population is a necessary ingredient of development? Plus the sources of origin cited presents a bit of a problem -- that 9.2 m from Eur Russia didn't do Russia much good, nor the 4.7 m from Spain and the 1.8 m from Portugal.
Anyway, even if it were true in the 19th century, it does not necessarily make it true for the latter half of the 20th century -- the operative period for "poor nations" trying to develop. The global and national conditions in the 19th and the later 20th centuries are very different.
In any case, factually, has there been such a reduction of the movement of people? Inflow into the OECD averaged 3.1 m annually in the 1990s -- which would translate to 210 m over a comparable 70 year period. But I've no idea what the composition of that inflow is -- largely internal movement within OECD or from outside OECD
Still, if one takes the US alone, I recall reading somewhere that the latest statistics show that the proportion of foreign-born in the US is, today, little different from what it was a century ago. One could argue that, if anything, in-migration into the US underpins US development -- especially if one takes the biophysical sciences and engineering as one of its central needs. And this draws out resources from the poor countries -- the Philippines might be such an example. The usual brain-drain argument -- although the draining may result in people working in manual occupations: Malaysia is an example where there are Bangladeshi computer science graduates working as petrol pump attendants!