From a SARS perspective, if you look at your income tax return (ITR12) you will note income code 4218 is specifically for foreign interest earned, which you need to to declare. The 2023 interest exception of R23,800 is not applicable to foreign interest.
From a SARB perspective, their exchange controls dictate that any SA business entity is allowed to open a foreign bank account if you conduct business abroad HOWEVER, any credits against such an account (except for foreign dividends) MUST be repatriated within 30 days. If you therefore have an SA business and have sales in the US (or any foreign country), the income earned from said sales MUST be returned to SA within 30 days from being receipted in the foreign bank account. There is no restrictions on earning foreign interest from a SARB perspective.
https://www.resbank.co.za/content/dam/sarb/what-we-do/financial-surveillance/financial-surveillance-documents/2020/Currency and Exchanges Guidelines for Business Entities.pdf
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In terms of individuals, any SA resident is allowed to open a foreign bank account for the reasons specified.
https://www.resbank.co.za/content/dam/sarb/what-we-do/financial-surveillance/financial-surveillance-documents/2020/Currency and Exchanges Guidelines for Individuals.pdf
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The conclusion is that nothing stops you from either as a business or as an individual to opening a foreign bank account or to earn interest on that account.
The fact that the US banks don't want to pay you interest has nothing to do with any SA policies or restrictions. It is Let's Go Brandon that is taking your interest for his own pocket. US banks also have their own policies so it may very well an individual bank's policy or the state's policy that stops them from paying you interest - it is not because the SA government (through the SARB or National Treasury) restricts this.