I do not understand what you mean when you say "few captive big cats have conservation value". Big cats are highly endangered, and while there are not many programs for releasing captive bred big cats back into the wild at the moment, assurance populations are always good to have. Additionally, ambassador animals kept in zoos are vital to zoo conservation programs and fundraising. The fact is people would be donating a lot less money to wild cat conservation if they didn't have captive animals to inspire them.
Based on ZTL, the number of zoos housing various forms of wild cats are as follows:
Jungle cat (Felis chaus) 33: Caucasian jungle cat (chaus) 1; Palestine jungle cat (furax) 4; Egyptian jungle cat (nilotica) 1
Sand cat (F margarita): Arabian sand cat (harrisoni) 26
Wild cat (F silvestris): Gordon’s wild cat (gordoni) 9; Scottish wild cat (grampia) 23; African wild cat (libyca) 1; East African wild cat (ocreata) 1; Indian desert cat (ornata) 1; European wild cat (silvestris) 141; Palestine wild cat (tristrami) 2
Pallas’ cat (Otocolobus manul): Siberian Pallas’cat (manul) 37
Canadian lynx (Lynx canadensis) 13
Eurasian lynx (L lynx) 125: Carpathian lynx (carpathicus) 44; Central Asian lynx (isabellinus) 7; Northern lynx (lynx) 207;
Siberian lynx (wrangeli) 16
Iberian lynx (L pardinus) 4
Bobcat (L rufus) 23
Caracal (Caracal caracal) 51: Common caracal (caracal) 17; Turkmenian caracal (michaelis) 1; Schmitz’s caracal (schmitzi) 2
Serval (Leptailurus serval) 138
Cougar (Puma concolor) 101: Missouri cougar (missoulensis) 2; Chilean cougar (puma) 2
Jaguarundi (Herpailurus yagouarundi) 29
Cheetah (Acinonyx jubatus): South African cheetah (jubatus) 118; Sudan cheetah (soemmeringii) 17
Geoffroy’s cat (Leopardus geoffroyi) 31
Ocelot (L pardalis) 60
Oncilla (L tigrinus) 3: Southern oncilla (guttulus) 2
Margay (L wiedii): Central American margay (nicaraguae) 1; Yucatan margay (yucatanicus) 16
Leopard cat (Prionailurus bengalensis) 3: Indochinese leopard cat (bengalensis) 14; Tsushima leopard cat (euptilura) 19; Palawan leopard cat (heaneyi) 5
Rusty-spotted cat (P rubiginosa): Sri Lankan rusty-spotted cat (phillipsi) 16
Fishing cat (P viverrinus) 43
Asian golden cat (Catopuma temminckii): South-east Asian golden cat (temminckii) 6; Tibetan golden cat (tristis) 2
Clouded leopard (Neofelis nebulosa): Indochinese clouded leopard (nebulosa) 42
Lion (Panthera leo) 245: Southwest African lion (bleyenberghi) 24; Southeast African lion (krugeri) 52; Barbary lion (leo) 29; Asiatic lion (persica) 44; Somali lion (somaliensis) 1; Kalahari lion (vernayi) 5
Jaguar (Panthera onca) 103: Amazon jaguar 1
Leopard (P pardus) 61: Caucasian leopard (ciscaucasica) 1; Indian leopard (fusca) 1; North Chinese leopard (japonensis) 27; Sri Lankan leopard (kotiya) 24; Javan leopard (melas) 4; Arabian leopard (nimr) 3; Amur leopard (orientalis) 54; African leopard (pardus) 5 ; North Persian leopard (saxicolor) 39; Central African leopard (shortridgei) 1
Tiger (P tigris) 168: Siberian tiger (altaica) 177; Malayan tiger (jacksoni) 9; Sumatran tiger (sumatrae) 53
Snow leopard (P uncia) 99
This gives a minimum number of individuals per species: Tiger 407; lion 400; Eurasian lynx 399; leopard 220; wild cat 178; serval 138; cheetah 135; cougar 105; jaguar 104; snow leopard 99; caracal 71; ocelot 60; fishing cat 43; clouded leopard 42; leopard cat 41; jungle cat 39; Pallas’ cat 37; Geoffroy’s cat 31; jaguarondi 29; sand cat 26; bobcat 23; margay 17; rusty-spotted cat 16; Canadian lynx 13; Asian golden cat 8; oncilla 5; Iberian lynx 4
There is a tendency for keeping big cats, rather than small cats. Can't visitors be inspired by small cats? What is the point of 'assurance populations' of mixed subspecies big cats, when ZTL lists no populations of small cats, even though various species were kept in the past? These include the African golden cat, Andean cat, bay cat, black-footed cat, Chinese mountain cat, flat-headed cat, kodkod, marbled cat and pampas cat. I have seen African golden, black-footed and pampas cats, but, like various other small cats, various zoos don't consider them worth keeping or saving, despite the fact that reintroduction programmes could be more easily achieved than with large cats.
More people are killed by cows than big cats in zoos.
There are many more cows in the world than there are big cats in zoos. Using your logic, more people are killed at home than are killed at home, so does that mean that everyone should be homeless?