As it includes Medicaid spending as federal benefit spending (and likely PPACA subsidies -- but I haven't gotten that far in the footnotes) the $10k would seemingly amount to just covering every American household's private-market insurance premiums (with no regard to whether they needed them covered and further handing 'free money' to healthy young childless households whose premiums would be much lower).
And without being structured as Medicaid, it would abandon the other (cost-controlling/bureaucracy-reducing/waste-reducing) financial benefits of a single payer health system -- benefits over the private market that Medicaid actually delivers (according to numerous studies).
So the end result is that poor people would see their net benefits ruthlessly slashed, (good luck buying food and shelter after you use that 10k for market-rate insurance) all so that middle-class people can receive a stipend that they don't need and a decrease in federal-dollar-per-hypothetical-unit-of-healthcare efficiency.
The most-charitable read of this proposal, is that it's the result of a naive person doing "black box math" where they seek some mathematical ideal in the re-arrangement of government payments -- without any regard to the benefits being provided, the cost-effectiveness of those benefits and whether the rearrangement is a practical improvement.
I mean, if we're spending $20k per poor person, and children are still going hungry, under what logic would redistributing it as 10k to every single person see any sort of improvement in the ultimate goals of things like keeping children from going hungry?
To not see the massive benefit cut to these people that we've currently defined as needing help, we'd have to assume that for every dollar in tangible benefits received by the poor, there's a dollar in bureaucratic overhead.
And why on earth would we accept such an implicit assumption, when the ultimate source of all these numbers -- the CBO -- has regularly assessed such administrative costs and never finds such waste? [1]
[1] e.g. SNAP, pointed to regularly in the CATO document source, has administrative overhead of less than 4.5% of total federal cost. So if the average SNAP-receiving household is getting $287/mo, the overhead is $13/mo. Under this proposal, food money going to the currently-snap-receiving household would drop to $143/mo, with $15/mo going to 9 households that don't need SNAP. In the name of "saving" that $13/mo. Most of us would look at the infeasibility of a household feeding itself for $143/mo and see their own $15/mo as a more egregious waste than the original $13. Which, cynically speaking, is likely to be a feature. Following such a programs initiation, it would be trivial to get voters behind the proposal to cut their own taxes by $15/mo, to save them the overhead of having the government take the money only to give it back as a stipend they don't need. The end result would be the massive benefit cut and the reduced taxes.
http://www.fns.usda.gov/pd/supplemental-nutrition-assistance...
(EDIT: fleshed out SNAP example)