Helicopter Money is (almost) inevitable. The only questions are: who does it; and when do they do it. And we can't (easily) tell when it gets spent, and what it gets spent on, because money is fungible and we don't observe counterfactual conditionals.
Let's make some ballpark-correct assumptions. Assume currency pays 0% interest, and the (stock) demand for currency is 5% of Nominal GDP on average. Assume NGDP grows on average at 4% (2% long run real GDP growth plus 2% inflation target). So the central bank prints currency worth 0.2% of GDP each year on average (=5%x4%). Ignore the costs of paper and ink and administration. (It doesn't matter whether the central bank's "currency" is printed on paper, or plastic, or on computer discs. But if that currency pays interest, we have to subtract the interest rate paid on currency from the growth rate of the stock of currency, to calculate the central bank's profits.)
That means the central bank makes (average) annual profits of 0.2% of GDP from printing money. Those profits must get spent, by someone, at some time. The only questions are: who spends them; and when do they spend them?