I can only say that your correction is an improvement upon my interpretation of your idea.
Definitely only allow extra stables to be built within cities. I still say they should consume a certain amount of net food (a little less than a house?)
Personally I don't think Alternative(Fantasy) Mounts should have buildable Stables beyond their natural Supply (Griffin Lair). However, if Stables (for say Drakes or Scorpions) were buildable in cities, they should be at least three times as expensive, using at least three times as much net food, and at least twice as large (taking up at least twice the amount of space in a city).
Perhaps the specifics of a Fantasy Mount's stables could have different costs depending on the amount (different costs, different sizes, and different production rates) ... Fantasy mounts should be more expensive by at least two fold (preferably four fold) and of course much rarer.
For instance ... in a large plain their might be 4 wild herds of horses in a vast plains region, each of which give +4 horses per turn via stables, in addition to +1 horse per turn for every 4 horses stockpiled. To build a wild Stables requires 50 wood and 50 rigma. An inner-city stables costs 2 net-food, 1 city square, 100 wood and 100 rigma, as well as 1 rigma per turn in maintanence. (wild stables allow +40 maximum horses, city stables allow +20, and you start with a natural base maximum- default of 10)
Meanwhile in a long mountain range there might be 1 Griffin weyr that allows itself to be domesticated (the rest are permanently wild, if there even are any other weyrs). To build a wild Weyr Stables would cost 100 wood, 50 stone, 80 rigma, and 2 gold per turn maintanence. Such a Stables would provide +2 griffins per turn. The maximum number of supportable Griffins within a stable is 20. Personally I think that should be it, only possible source. However, if you wanted to build a Weyr in a city it would consume 4 net food, 150 wood, 100 stone, 200 rigma and a maintanence of 4 gold per turn ... only providing +1 griffin and a global +10 maximum griffins. Griffins stockpile (if there was actually a large enough maximum for this to matter) would provide +1 griffin per turn for every 20 griffins ... however to see this effect you would have to reach a maximum of at least 30 or more, and even then its a minor detail because the rate is so low.
Essentially, you wouldn't be able to make a hoard of griffon riders unless you devoted the majority of your empire to it, Specialized in Griffon Riding (and the economy to support the expensive endeavor).
Personally I think global maximums for X mount should be enforced on all active units. Essentially, if you have a global maximum of 50 horses, and you already have 50 horse riders, your stables aren't making any more horses. I think this would decrease the unrealistic "need to spend". But take it all with a grain of salt, we don't really need maximums under the initial system anyways.