Each of my zoos (3 in franchise), have at least two exhibits for each species. A main habitat and a retirement area. I play like every species is endangered, and therefore I can't 'waste' any genetics, which means the only animals I purchase are for breeding. No 'filler' animals, unless they're born in my zoo. At least 10% of all animals born in my zoo have to be released to the wild and those released have to have the best genetics I have, save the breeding stock. Since I have to conserve all genetics, I keep one female (or male, if that's all I got from the mother or if he has really good genes). I also keep spreadsheets with family trees, so every offspring born in my zoo can be traced back to the original starting animals I purchased. Despite this way of playing, I don't normally have any tons of any one species in the trade center, because I sell or release them, or transfer them to another zoo, and only allow myself 1-2 of each species in the trade center.
However, my trade center is ALWAYS overflowing, because: 50 Species of animals in the game, even if you have 1 each in there, that's your trade center capacity. I keep 1-2 backups in case something catastrophic happens to my breeding stock. Or you need a fresh male or whatever. Now, I could open a storage zoo... I did try at one point. But, call me lazy, it seemed like SO much hassle to 1) put my animals in the trade center, 2) load the other zoo, 3) build an exhibit, 4) place the animals, 5) load back into my playable zoo, 6) 10 min later I need a different animal so I 7) load back into the storage zoo, 8) Repeat, repeat, repeat... And then you have to write down the genetics and figure it out on paper who's a good match for who... I just found it too tedious and immersion breaking. And then I tried quarantines for storage, but 1) the guests protest that, and 2) you can't see the animals genetics while they're in there.
I agree we shouldn't have unlimited storage, but I personally don't find 2 slots for each species excessive, instead of the 1 we currently have.