They do - quite aggressively. It lets the localized producers sell at quite a markup, and a lot of the GI/DOC designations are protected at the level of international treaties.
They seem to be more effective because there's a very direct cost/benefit to the GI-protected producers when people infringe. IANAL, but I suspect that because it's a WIPO/WTO treaty issue, it's also probably easier to prosecute than a very generic claim that someone is mislabeling "white tuna", again because the incentives are aligned for producer to show that they're being damaged by the forgery.
http://www.gourmetretailer.com/top-story-profiles___trends-p...
WIPO and WTO handle a lot of them: http://www.wipo.int/geo_indications/en/
They seem to be more effective because there's a very direct cost/benefit to the GI-protected producers when people infringe. IANAL, but I suspect that because it's a WIPO/WTO treaty issue, it's also probably easier to prosecute than a very generic claim that someone is mislabeling "white tuna", again because the incentives are aligned for producer to show that they're being damaged by the forgery.