Cheaper, mass produced musical instruments, like many other goods, were made more affordable by advances in mechanization, utilization of steam power, standardization of interchangeable parts, and other advances that were part of the industrial revolution. I'm not sure a line could be drawn between that and Rameau's insight that bass notes (i.e., inversions) did not determine the identities of chords.
Did Rameau's ideas contribute to a greater use of concerted chordal voices and the reduced use of counterpoint? I'm not convinced that the historic ebb and flow of complexity versus simplicity, which has occurred several times in western musical history, depended primarily on Rameau, though his ideas may have contributed.
Likewise, social changes beyond the work of Rameau may have had a stronger influence on popular access to art music than the work of any single composer or theorist. Rising standards of living, the French Revolution, the decine of land-based wealth and rise of a middle class, and other changes that shifted the balance of disposable income and the availability of leisure time are more likely candidates.