There are much stricter rules now, KYC on exchanges etc. But up until 2017/2018 I'd say the tax authorities weren't paying much attention and I'd be surprised if people with money who wanted to get it out didn't take advantage.
Does KYC on exchanges stop you from taking your money out of the country if you earned it legally in the first place? I'd think that the process would go like this:
1. Transfer the majority of your legally earned savings in rand, on which you have already paid taxes, from your South African bank account to a South African coin exchange, using it to buy Bitcoin, or Dai, or Ethereum, or whatever. Since this is white-market money, KYC should be no problem, right?
2. Transfer your Bitcoin (etc.) to a wallet or wallets you control, maybe with multi-signature authorization, maybe using an Electrum seed phrase, etc. Presumably this is what an exchange is for, right? Buying Bitcoin and then sending it somewhere.
3. Move to New Zealand or the Netherlands or wherever your new job is.
In 2017/2018 people could just go to a bank, or one of the many foreign exchange companies that operate in SA, and transferred their money anywhere in the world, legitimately. Exchange controls have been largely done away with for individuals.