Why do politicians in developed nations prefer foreign trade policy to income redistribution to counteract income inequality resulting from globalisation?

Why is, in developed nations, foreign trade policy favoured to direct income redistribution to counteract rising income inequality resulting from globalisation? Foreign trade theory suggests that a politician's wisest policy was to capture all welfare gains from free trade and to redistribute some of the winners' gains to the losers. By implementing votes and budget maximisation goals of a politician into the analysis, it is shown that, in fact, it might be politically reasonable to redistribute income indirectly through trade policy. However, this will be identified as a potential rationality trap demanding for institutional changes of the global trade architecture.