High food and low hammers always means whipping to me. Although DaveMcW has said a few times that only a granary is necessary in a commerce/cottage city and then from there max growth + working as many cottages as possible is the way to go. I would imagine at the health cap you could whip additional science/gold buildings.
From my experience, cottage growing (in pure cottage cities, i.e. the ones you get the feeling that will not amount to much food/hammer wise) is better than whipping in most cases. For me at least (and I am admittedly no elite player) a CE gets its wings around the time where you get democracy and can start rush buying (I'm assuming you don't have pyramids).
You can just buy all those buildings, and with the gpt your cottages are earning its just about 20 turns to upgrade all your core cities to any buildings you desire. Those worked cottages will then pay infinately more than the buildings you would have whipped earlier, since you just got the buildings essentially "gratis" (in the sense that it didn't affect the city negatively in any way).
As I see it the +25% research/gold for library/market, is decisively important only after gettings many towns+Free Speech+PP, rather than in a city with a bunch of hamlets.
If you have a great local surplus of heavy food like pigs/corn, you can when necessary just plant your cities so they can share them at BFC corners.
The democracy buying spree occurs around 1100-1200 AD for me but it's very possible more skilled players get this effect around 1000 AD or even earlier.
I'm also subconsciously thinking about the isolated/semi-isolated CE I always tend to end up for some reason. On tighter games, with aggressive neighbors I do use the whip extensively to get barracks/forges/units/culture spread.
I would, however, guess that the "only a granary" maxim is slight hyperbole. courthouses are nice and there usually are enough forests to support them.