From Bruce Haynes’s The Eloquent Oboe: A History of the Hautboy, Oxford University Press, 2001:

In the seventeenth and eighteenth centuries, a wind player was an hautboist who might by circumstance be led into a concentration on some other type of instrument. The modern idea of a musician who would limit himself to one instrument, and become a virtuoso on it, took hold at the Dresden court at about the beginning of the eighteenth century, perhaps as a result of the numerous Italian musicians who worked there, and who tended to specialize. But it remained unusual in Germany for some time.

More insight from the footnotes:

Based on archival evidence, Oleskiewicz (1998: 49) believes woodwind doubling ‘completely disappeared sometime between 1717 and 1719.’

And:

There is evidence that hautboy players in bands in the early 18th c. could not necessarily switch to bassoon.