I am not convinced by this sort of top-down analysis. To start, by looking at total funding it hides several problems with the entire system.

As I learned from the US healthcare debate, an astonishingly high percentage of the money goes into overhead. For example, you pointed out SNAP.

https://en.wikipedia.org/wiki/Supplemental_Nutrition_Assista... says: "SNAP benefits cost $70.9 billion in fiscal year 2016 and supplied roughly 44.2 million Americans with an average of $125.51 for each person per month in food assistance."

So, $55.5 billion goes to Americans, meaning %15.4 billion or 20% is overhead.

How much of the other money is also overhead? Consider a charity which takes in $100M to "build homes for the poor", and ends up building 100 such homes. Your analysis suggests the poor are receiving $1M homes. On the other hand, if 95% of the money is spent on overhead, they are only getting $50K homes.

We know there's overhead elsewhere, though not 95% - that was used to make a point. For example, your Medicaid example is directly connected to the absurd health care costs in the US. As Wikipedia tells me: "In 2011, there were 7.6 million hospital stays billed to Medicaid, representing 15.6 percent (approximately $60.2 billion) of total aggregate inpatient hospital costs in the United States.[74] At $8,000, the mean cost per stay billed to Medicaid was $2,000 less than the average cost for all stays."

So part of that Medicaid spending is on an overpriced medical system. Another part of that spending is simply wasted in carrying out means testing and administrative overhead. These are costs which don't exist in the healthcare system of most other rich countries, and in neither case should it be viewed as money going towards poor Americans.

Furthermore, means tests requires that applicants do extra work to file the right forms, stand in the right lines, and in general deal with the bureaucracy. This can include taking time off of work (so getting paid less), trying to find a baby sitter, etc. These are monetary costs which are hidden in your analysis, which only looks at the government costs, and there are human costs of extra stress and hassle - and issues related to loss of respect and humanity aren't easy to quantify monetarily.

To get back to your text, you use numbers like "There are approximately 16 million households that qualify as poor in the US" and "you instead distribute that figure among the bottom quarter of adults". However, as DanBC pointed out from the Forbes article, the denominator "the number of people who claim benefits", gives $24.77 per day.

That suggests that there are many more people who claim benefits than your estimates suggest. I can see one place already. You limited the denominator to the "bottom quarter of adults .. under the age of ~65 [because] over 65 most are drawing on Medicare." However, https://www.ssa.gov/history/pdf/RowlandandLyons.pdf points out that 9% of the elderly draw on both Medicare and Medicaid.

About 185M people are between 18-65 years old. (Adding up https://en.wikipedia.org/wiki/Demography_of_the_United_State... ). 1/4th of that gives about 46M, which close to your estimate of 50M ($1T/50M people=>$20K/person)

About 46.3M people are enrolled in Medicare due to age. 9% of that is 4M, so that's 8% missing from your earlier numbers.

In addition, children in "[a]ll states - except Tennessee - have additional disability-specific eligibility criteria, which allow some children with disabilities to qualify for Medicaid even if their parents’ income exceeds the state-established threshold." https://www.americanprogress.org/issues/early-childhood/repo...

I think this would also affect your numbers by increasing the denominator and so lowering the overall per-person payments.

To go back to DanBC's point, why aren't you using "the number of people who claim benefits" as your denominator?