The browser can simply store a collision resistant hash (e.g. SHA-256) of the body, if it wants a smaller cache key. I can't really think of any caching related attacks that don't equally apply to a query parameter. Generating a unique 30 character query parameter is just as easy as generating a 30 MB request body, if you want to flood the cache.
Not necessarily that simple, as you'd have sort all the input parameters to maintain a useable cache key. Not especially difficult, but if the data is large and so re-allocation and sorting is required, then you're starting to open up the attack surface where bugs might have been introduced.