You know, increasing HDI could just decrease the standards of HDI... that's the problem with using metrics like that instead of something physical to change.
Doubtful. The beauty and fallibility of HDI both lie in its simplicity. It's just a composite measure of three numbers: average life expectancy, GDP per capita, and years spent in school. The first is impossible to fake, the second is difficult to fake if you use a benchmark currency to measure GDP (this is susceptible to stuff like exchange rates that have more to do with economic (mis)management than quality of life, but it's still a useful way to compare economic development), and the third is...well, honestly not the most cut-and-dried metric, but it still tells you something, since every kid in school is a kid who's not working in a factory, even if the schools aren't very good.
There are downsides to this! HDI tells you nothing about gender equality, corruption, political instability, freedom of expression, or all sorts of other important things. These influence HDI indirectly, but not absolutely, and it's definitely possible for a highly developed country to be a totalitarian hermit state (Cuba), ridiculously corrupt (Argentina, southern Italy), or disgustingly misogynistic (Saudi Arabia). But that's kind of the point- those are more abstract and difficult to measure. HDI is simplistic, but it uses a standard that can be applied everywhere.
There might be even quicker and less disruptive ways to develop the world en masse. If you think of world GDP as a function over time, then the total amount of
assets in the world is the integral of that function.
XKCD informs us that the estimated total value of humanity's liquid assets was about $77 trillion- and that was in 2011; let's say it's about $85 trillion or so at the current moment.
Increasing the size of the world's liquid assets by 1% would give you a check for about $850 billion dollars a day, which would buy you pretty much any public works project you needed. If it were distributed evenly, it would be about a $120 check for every person on the planet today. Hello, basic income. (You can always use your powers to keep a lid on inflation if you need to. I'm not an economist and have no idea how much inflation this would cause.)
I'm starting to think this would make a good movie. Being able to magic up $850 billion a day gives you wealth on a scale that makes John D. Rockefeller look like a Bangladeshi street child, and with godlike wealth comes unbelievable power. There'd have to be some catch, though. Maybe the protagonist forgets about inflation and turns the world into Weimar Germany by accident?