Considering that Stripe was originally known for letting websites accept credit card payments without seeing your credit card number, one might assume that Stripe Identity only allows websites to see the verification result, and not your selfies and scans of your identity documents. That would be an incorrect assumption. Per https://support.stripe.com/questions/managing-your-id-verifi... customers of Stripe Identity…
Edwin from Stripe here. The two cases are actually very similar. If you want to avoid ID documents ever being stored on your servers, Identity makes it easy to do that. (Just as Elements/Stripe.js makes that easy for card numbers.) On the other hand, if you want to score card numbers or ID documents (and there are sometimes good reasons for doing this!), Stripe makes that straightforward.
If you want to export credit card numbers from Stripe, you can only have it transferred directly to another PCI DSS Level 1-compliant payment processor, and Stripe imposes rather strict requirements on the transfer: https://stripe.com/docs/security/data-migrations/exports#whe...
If you want to export ID documents or selfies, you can just make an API call or use the web interface. This can and will be abused.