This is most assuredly NOT true. In fact, free trade helps corporations at the expense of people by turning wages into a zero sum game with the peoples of different nations competing with each other for who can work for less. Large portions of the masses of Bangladesh, Thailand, Jamaica, China, etc., went from subsistence farming in the countryside to diseased, polluted shanty towns where they don't have enough to eat. Sure a very small segment of these societies prosper, but that is not good enough to justify impoverishing and sickening the vast majority.
Actually, most all of these trade barriers, tariffs in other words, are gone already. TPP is more about US companies dominating via patent and copyright expansions and locking poorer nations into being police for US corporations while opening up even more of their national livelihood to corporate domination: if a nation wants to provide a service of benefit directly to their people forget it, the TPP doesn't allow for expansion of social programs. Companies will be able to sue poor countries for "lost expected profits" anytime a nation passes an environmental law or wants to regulate an industry they can be sued for massive "damages". The history of "trade agreements" from NAFTA onward have been a travesty for first world workers and third world workers alike. And the TPP helps to cement these changes in place while gutting sovereignty once and for all.
If it was merely about cheaper sneakers for the poor you might be right. Unfortunately the reality is much worse than the fantasy you've been fed. Ask yourself, when has the global corporate structure ever done anything that helped the people of the world over its own bottom line? Given that the global corporations are salivating over this TPP it is obvious who will benefit. And who will suffer.