On 7 March, the House of Lords debated a motion, moved by Lord Blunkett, to take note ‘of the contribution of higher education to national growth, productivity and levelling-up’. Given the number of peers who had signed up to speak, each backbench speaker only had five minutes.
In my speech, I decided to make two principal points, each designed to draw attention to the value of higher education beyond that of the economic, encompassing personal development – society is stronger by having a well-educated (and, a point touched upon by Lord Willetts, more resilient) population as well as benefiting politically, and not just economically, by the export of higher education. Having overseas students attend UK universities not only benefits local economies and university research, but also trade and soft power, increasingly important as our capacity to exercise hard power declines.
I also touched upon a point I have developed before, namely that there is more long-term benefit in using our overseas aid budget to bring students from developing countries to study in the UK, who then return home to the benefit of their nation, than there is in giving money to the governing regime. We also need to recognise that in recruiting overseas students, we are in a highly competitive market.
The Norton View 
My father studied at the University of London, Kings College School of Laws. Another of his friends did the same from our small town. Each went on to build very different networks of people around much of the world.
My mother wrote a couple of books that many in Family Missions Company read and discussed around the world and those books discussed our time in the UK. Millions of dollars areoved around the world each year by that one nonprofit. His friend I mentioned supported a network of writers and scholars and artists not incorporated.
I have remembered and mentioned my time there as his young son and my own studies in London and my uncle has done the same as to his time in a UK boarding school. Neither my uncle nor I would have studied there but for my father studying in a graduate program in Laws.
While the world is complicated it seems clear to me that your argument about soft power is valid from my own set of references.