West Indies: Hasn't had a good spinner since Gibbs, and Warne didn't seem to have had an effect. Nor have they looked like they want a spinner.
India: Always had a vibrant and rich heritage of spin bowling, which has always been taken as our main weapon.
Pakistan: Qadir and Mushtaq Ahmed were already operating there in the 80s and 90s, and the tradition there was vibrant as well.
Sri Lanka: I cannot say for sure, but Somachandra De Silva was there, plus they too have historically depended on their spin attacks more than their pace attack, so they, like the two above, knew the importance of having spin in the attack. If anything, India and Sri Lanka always wanted better pacers.
South Africa: Since Tayfield, they have never been blessed with a good spinner. If the importance of having a spinner increased in South African eyes after the emergence of Warne, then I wouldn't know. Do you know for sure?
New Zealand: Same as SA.
We are left with England and Australia, where what you say is almost definitely true for England, and definitely for Australia.
Do you think that something which most probably happened only in England and Australia can/should be taken to represent the world of cricket at large?