At this point you might be right, but the origin is about wanting to fit in with the new french overlords.
In regular language, you would call porc the meat that comes from a cochon, and bœuf the meat of a vache.
It's not as clear cut as in English, as a bœuf is also an ox, and you can also call a pig a porc, but I think it indicates that the linguistic distinction between an animal and its meat is indeed at its core a dehumanizing process, it might just have been helped by the French-speaking rulers of England, but it still happened in France eventually, more recently and without exterior intervention.
Why? I feel absolutely no emotional difference between "cow meat" and "beef", and would be surprised to hear that it really made a difference to pretty much any non-vegetarian... Further, it seems nobody has felt the need to introduce a different word for 'lamb' - it's still an extremely popular meat despite the word literally meaning 'baby sheep'...
I think it's drawing a really long bow to think it's desensitising language (dehumanisation isn't really the right word, since cows, sheep etc. aren't human). At the end of the day, I think it's just a quirk of language development...