If taken seriously, locavorism would not only mean lower standards of living and shorter life expectancies, but also increased environmental damage.
Think of it this way. Because nobody would bother transporting foodstuffs over long distances if it didn't deliver superior outcomes, locavorism can only result in higher prices and less variety. A less varied diet is inevitably less nutritious. Higher prices also leave less money in local pockets to spend on other things, in the process destroying jobs both at home and abroad. Furthermore, foreign food exporters no longer have the means to purchase other goods produced in the locavores' community.
In addition, producing food in the most suitable locations and delivering it over long distances is actually much "greener" than growing vegetables or manufacturing dairy products locally. The "local" operations require energy-guzzling heated greenhouses instead of natural heat, massive amounts of irrigation water rather than abundant rainfall, and large volumes of animal feed to make up for less productive pastureland. It's better to grow tomatoes in the Florida sun than in a heated greenhouse in upstate New York because the energy required to transport them 1200 miles is only a fraction of that required to heat greenhouses for several weeks.
The most preposterous claim of locavores is that their prescription increases food security. Yet, no local food system can ever be completely protected from insects, plant and animal diseases, drought, floods, earthquakes and other natural catastrophes. Fortunately, trade liberalization insures that the surplus of regions with good harvests can be channeled to those with below average ones. In the long run, good and bad harvests cancel each other out. Locavorism, by contrast, puts all of one's agricultural eggs in one regional basket.