An invasion would mobilize the United States

Why not use troops from India to invade the United States?

Because invasion would provoke the large American mobilization that Britain had seen during the Civil War, making a difficult war much larger.

Sending imperial troops to invade the United States is rejected as strategically self-defeating. Britain's observation of the American Civil War showed that the country could organize very large armies once sufficiently provoked. An invasion would create that provocation and overcome the inertia on which the counterfactual depends. Leaving the United States alone is therefore presented as safer than turning its latent manpower into an active enemy army.