I don't think the Imperial Truth was 100% devoted to starving the Chaos Gods of worship, since as you've said, they don't need to be worshiped (though it certainly doesn't hurt). I think the Truth was geared more toward minimizing the influence of the Chaos Gods while sheltering humanity through its transition into a psychic species.
The Emperor did everything he could to minimize the necessity of psykers, which at this point in humanity's evolution, were quite unstable. The Council of Nikea got rid of Librarians and practicing sorcery, and once the Imperial Webway got going, there would be no need for astropaths. Ships wouldn't need to take a shortcut through a demonic hell in order to get to other worlds. Meanwhile, the Black Ships bag 'n' tag every psyker they can get their hands on. All of this was because the Emperor knew that humanity wasn't ready for this radical evolutionary step, and without his guidance, there would be unchecked demonic invasions into physical space, possession, mad psykers going out of control. Basically everything that's happening in the year 40,000.
I don't think the Emperor was going so far as to starve the Chaos Gods, but he was definitely taking steps to protect humanity from their influence.