There might well be good reasons for diverting vaccines to third world countries, rather than using them here, but I fail to see the logic in "from where potentially scary mutant variants are more likely to arise".
The alpha variant was first detected in the UK, beta was initially spotted in South Africa, gamma was first found in Brazil, delta in India and, although the first instance of delta is recorded by the WHO as 'multiple countries', it's primarily associated with South Africa. So there's a good mix of 'developed' and 'less developed' countries there.
I see no reason why the next 'variant of concern' is more likely to originate from Uganda than it is from the United Kingdom, or why it's more likely to come from Afghanistan than it is from Austria.