I know this pattern and have used it myself. The problem is though, that generally you should only throw an error when you reach an exception - it's like saying "I don't know what to do next", and you defer that decision up the stack.
Is a request that technically succeeds (the response has come back), but has a status code where the server has indicated something didn't work always an _exception_ in your client code? I'd argue it isn't, and should just be handled in the normal control flow of your client code via conditionals.