Much of the unstated benefit of locally produced food is in a shorter time between harvest and plate (fresher), less handling (bruising), less transportation (ecological), less packaging (resources + cost), shorter supply chain (less middlemen; farmer/producer should receive higher % of retail price), generally more pride and care involved (better quality) plus of course supporting the 'local' economy by keeping the money circulating locally and local smaller family farms in business.
For animals it should mean quicker time-to-kill (less stress) due to less travel and coral-ling at abattoirs, and, depending on the butcher, better cuts of meat (less mechanical cutting) due to following the grain.
In the U.K. the biggest immediate benefit is the farmer receiving a greater slice of the retail price, which is essential in some sectors (such as dairy) where many farmers receive less than the cost of production, and certainly not enough to protect against poor years.
Combined with low investment returns pushing capital into land 'investment' which is driving land price growth to ridiculous levels; subsequently driving rents for farmers who don't own their own land to bankruptcy levels (we recently sold 10 acres @ £10,000/acre which was bought for around £2,500/acre 15 years ago [0], but the gross yield hasn't moved from around £400/acre).
Even amongst farmer land-owners many are selling off small parcels in order to cover shortfalls in farming income or to invest in new facilities and equipment.
The big farming agri-businesses (10,000+ acres) are about the only ones that have the production scale to make profits and invest in land.
Born-n-bred and still living on a 1,000 acre farm, but hacking code.
[0] http://pdf.savills.com/documents/Savills-ALMS-Feb-2014.pdf