Fairly sure that would be considered a breach of patient confidentiality where I live, at least.

Oh just wait, the AI phone service on their side will be more than happy to complete your device attestation key challenge by touch tone. We have to make sure you are still you after all!

But in all seriousness, many services are making it difficult through to impossible to communicate outside of their web or app platforms. Call centres are expensive and messy, and it's now apparently acceptable as a society to treat customers/clients/whatever as adversaries so they can get away with making it hard to communicate with them.

Or ask for a print out.