Apparently not because of concerns about expired or contaminated food from untraceable sources, but simply because the city can't control the nutritional value of donated food. God forbid homeless people have access to a Twinkie.
Bloomberg's an odd (and with a net worth of $25B, obscenely wealthy) cat - lifelong Democrat until he turned Republican for the 2001 mayoral election (which happened to coincide with the 9/11 WTC attack); declined the use of public campaign funds, so that he could use his own vastly larger financial resources - he spent 5 times as much on his mayoral campaign as his opponent; has implied he views the $1B/year NYPD as his "private army"; has declined the mayoral salary, opting instead to take $1/year compensation for his mayoral services.
Another interesting thing I learned today: the second-largest privately held company in the U.S., held by the folks who brought you the right-wing lobbyist outfit "Prosperity for Certain Americans" (although they call it an "advocacy group" and the name on the door is "Americans for Prosperity"), and that right-wing would-be "grassroots movement" which turned out to be more like "astroturf", the Tea Party - yes, the Koch Industries conglomerate with its 70,000 employees is considered a "small business" for tax purposes. What's in a name? Why, a 20% tax dodge, that's what. 20% of annual profits that hover around $100B, do the simple math and that's $20B/year tax revenue tucked back in Koch Brothers pockets because "small business" doesn't mean what it says at all.
Food and poverty
Looping back to the question of feeding the homeless, though: 2012 national average monthly food expenses on a "moderate" food budget for adults age 19-50 years was just about $275, or $3300/year. Children and the elderly eat less, but the nation as a whole could use to eat healthier, and money really is what stops a lot of people from eating more fresh fruits and veggies, organic grass-fed meat, and wild cold-water fish. So, multiply that $3300/year by the nation's population of 310M people, and you get... ouch, 1.02 trillion dollars.
How much is a trillion dollars? OK, if we want to feed the nation, then maybe we have to think about scaling back to a $220/month "low-cost" plan or even a $170/month "thrifty" plan. $170 still buys a LOT of beans and rice, which can be rounded out on the cheap with whole chickens and fresh-frozen veggies. A year on the "low-cost" plan costs $2640 per individual, or $818B for the nation. A "thrifty" person-year is $2040, or $632B per USA.
The USDA stats tell us what people spend - but not how much of the end consumer cost represents middleman markup (100% between farm and fork is likely), profit margins, and costs of inspection, preservation, packaging and distribution. If children in remote, undeveloped and drought-blighted parts of the world can be sustained on a dollar a day, or $365 a year, then surely it can't cost ten times that to supply an adult in an industrially developed nation, amidst efficient engineered farms and processing plants, with food enough not merely to subsist, but to thrive.
So let's imagine, with smart social planning and investment in agritech to keep farms smallish, local and producing sustainably year-round, that we can pare out that 100% middleman markup. Maybe cutting out wholesalers isn't enough; maybe we'd also have to ban speculation in food futures markets (we know speculation in petrofuel costs the consumer as much as 30%). Maybe we'd have to apply to food distro, or at least specialty food distro, the alcoholic beverage distro model of states like Alabama, New Hampshire, Virginia, Oregon et al. where the state holds a monopoly on operation of liquor stores; or Iowa, where the state holds a monopoly on wholesaling of distilled spirits.
Whatever the means, I'm certain there's no reason a box of Cap'n PedoBear Corn Starch Puffs, now with more sawdust and HFCS, and which your kid would happily eat in one weekend-long binge, has to cost $4-5, plus another $4-5 for a gallon of milk (the lactose in which gives your kid cramps and diarrhea, though he hasn't made that mental connection yet.)