Does anybody use ETL-for-marketers tools to extract User data from one source, then load it into Stripe as Customer objects?
I don't think it's common. We mostly see developers creating Stripe Customer objects themselves in their backend.
If I understood your original question correctly, you were asking why ETL tools don't do this? I think it's because these tools are deliberately capable of working with fuzzy data streams, so it at least feels weird to start using them for secure actions. Their security model may also make it dangerous to try.
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Somewhat aside: Authenticating actions from the client is most-easily solved by signing JWTs. Tools like Hasura are doing this in the wild, though it isn't too common among third-party APIs yet. Another close example is Intercom, which asks you to use a non-JWT signature to pass in user data: https://developers.intercom.com/installing-intercom/docs/ios...