Yes, this period was influential on policy, but perhaps not in the ways you may think. I think that one of the big influences was on education, more specifically the white-washing of the US's history of colonialism in the islands. It cannot be forgotten that the US came to the Philippines as a conquerer and toppled an already-established government by way of a bloody war and then the violent oppression of other Filipino groups throughout the period. What the US has done in policy is change the narrative from one of colonial endeavor to one of liberation and aid. The invasion was recast as a benevolent invasion, existing to teach the Philippines about demcoracy and prepare the people for self-governance. Why this was important: it continues to inform how Americans view their past moving forward. The manipulation of education policy regarding this has arguably contributed greatly to the US repeating reprehensible foreign policy decisions. The other big influence was on colonial practices in general. In the Philippines we can see the beginning of neocolonial practices, rather than traditional colonialism, and that is what I want to discuss below.

Now as to Taft's time in power in the Philippines. Daniel B. Schirmer argues that Taft presented a new form of colonialism when attempting to conquer the Philippines. He combined military suppression with a paternal position of guidance. Why? Because this rejection of open racist hostility made it easier to work with Filipino elites. Taft wanted to create a strong base by finding powerful, willing collaborators in the Philippine population. Behind the facade of "self-governance" goals, this also divided Filipino nationalists. Among the policies was the raising of a Filipino military force, led by Americans. These troops would be more effective: they knew the languages and terrain, and it would help gain support because Filipinos were taking an active part in the creation of this colonial government. In contrast to the Spanish, who never allowed Filipino representation above the municipal level, Taft found elite Filipinos who were willing to sacrifice sovereignty for political gains. This collaboration was considered the peak of success: it was proof of the Filipinos' subordination to white authority, and their desire for it. The census, for example, was a tool for fostering more collaboration, as well as "testing" the Filipinos' ability to be accountable to the hierarchy. Taft referred to Filipinos as "little brown brothers" and spoke of their intellectual inferiority; of course this played into the civilizing mission. This was all predicated on being able to supervise Filipinos, turning them into civilized people through American supervision and orders. Taft attributed the ability of Filipinos as "natural imitators" to the fact that they were "Orientals". As other "orientals", when their confidence was won, they would follow obediently, or so that was the belief. I think you can see, however, how this is different than traditional colonization. Taft put Filipinos in much higher-ranking positions than in a traditional colonial system and cemented his influence by gaining the favor of the wealthy and educated elite Filipinos, and creating a system where American power was more insidious than outright. This is absolutely the blueprint for later neocolonialist policies after the official end of colonization.

Sources:

"The Conception and Gestation of a Neocolony" by Daniel B. Schirmer in The Philippines Reader: A History of Colonialism, Neocolonialism, Dictatorship, and Resistance edited by Daniel B. Schirmer and Stephen Rosskamm Shalom

White Love, and Other Events in Filipino History by Vicente Rafael

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As for reading suggestions, the two books I cited above are great, but I will add some more here:

Body Parts of Empire: Visual Abjection, Filipino Images, and the American Archive by Nerissa S. Balce

American Workers, Colonial Power: Philippine Seattle and the Transpacific West, 1919-1941 by Dorothy B. Fujita-Rony (this one focuses on Filipino immigrants during the colonial period, but I think it is also very important to understanding how this colonial period operated)

Making Moros: Imperial Historicism and American Military Rule in the Philippines' Muslim South by Michael C. Hawkins

Motherless Tongues: The Insurgency of Language Amid Wars of Translation by Vicente Rafael

The Star-Entangled Banner: One Hundred Years of America in the Philippines by Sharon Delmendo