In the closed source extension mentioned by [deleted] I actually implemented anonymous poll votes, which are somewhat similar.
The problem/limitation with that feature is that if people have a bit of know-how, they can bypass any sort of limits you might want to put (per cookie, per IP, ?). So if you provide some incentive for anonymous likes, it's guaranteed it will be abused by people anonymously liking their own posts many times.
Also, that wouldn't be possible with the bundled Flarum likes extension because there's not really any concept of likes counter. It's just a list of users who liked. So you can't have anonymous likes without rewriting the extension itself to be count based instead of user-based.
