Niall -
The first statement of what we would call today "strategic" architecture appeared in Britain early in 1901. Those discussions/arguments predated the arrival of the Haskell, which did not arrive in the UK until late 1901. The ball was not widely available in the UK until the next year, 1902, and thereafter became wildly popular.
Strategic gca is best understood as response to unhappiness over what we call today "Victorian" golf architecture. The sides taken pro or con over the new design ideas did not align very clearly with sides taken over the Haskell. Some opposed the Haskell while defending older Victorian design ideas (Taylor, Hilton). Some opposed the Haskell while advocating the new design ideas (Low, Croome).
(Adam will know better than I about Colt's views of the Haskell, though I think Colt was anti-Haskell, yes?)
The Haskell did require the lengthening almost all golf courses from about 1903 into the 1920s. The course revisions, in turn, forced many clubs to pick a side in the larger architectural debates. Which then spawned further debates. Sandwich is a good example where course changes were needed to keep up with the more powerful Haskell (think: the depressing changes to the Maiden) while at the same time the club wanted to stay true to Laidlaw Purves' Victorian design ideas. Among the issues clubs like Sandwich faced was whether to move cross bunkers or other cross hazards farther down the fw or build 'side' bunkers based on a very different approach to golf course design.
The above egregiously simplifies a couple of fascinating decades. The Haskell had a role in all that, but the longer ball was not why basic architectural ideas were rethought by Low, Colt and others. That rethinking was undertaken because of the dissatisfaction with older design ideas. The American ball accelerated the implementation of their new architectural ideas on many existing courses.
Bob