It's absurd how difficult simple concepts are on the FES. The like are mistakenly worth something to the buyer but they are actually worthless and the only benfit-or from click farms is the click farm that makes money off the likes. Because the like are not genuine, they are not real impressions and they don't turn into anything beneficial for the page owner. We are not talking about economics here. In that regard you would be correct, but this is about SEO.
I understand what you're saying perfectly. I was merely refuting your claim that the likes were worthless.
In fact, as PP alluded to, a like farm could randomly like your page multiple times. This in turn makes you seemingly more popular to search engines than pages with fewer likes. This, in turn, means that legitimate people will more likely visit your page and hopefully like it. As the more people like it, the higher it goes in the search results and the more likely other people will see it and like it.
Once the likes have reached a point where it's statistically unlikely to be mostly click farm likes, the page will thrive on it's own and any click farm likes become statistically irrelevant.