If I may pop in on this clever query, the linguistic form of "drink" is an Action Noun, hence the usage of the term is exactly what you would wind up doing with it (you will be 'drink-ing' the 'drink') whereas the term "food" is not an Action Noun, it is a conceptual Noun ('regular' noun), where the term does not imply action, only an existence of an entity; thus, it simply cannot be used in the same way (Yay English).
The 'action' form of the term "food" would more likely be the Plural Noun "eats" - as in the idiosyncratic phrases "get some eats" or the even more informal "that was some good eats"; in which case then, using 'action' forms for both terms, you would in fact then find yourself 'eat-ing' the 'eats'...
This double-usage of the various forms of nouns is further shown by the phrases "get a drink" and "get some eats" - and the now-easily-seen related phrase "get some food". Still, this was a great question and yet more evidence of the befuddlement of The English Language
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