I get parent comment's totally legitimate security concerns. And businesses that have no business having my identity should surely not be asking for it. But I don't honestly understand how this has anything to do with Stripe. These businesses (which for whatever reason are asking for ID verification before doing business with you) are just using Stripes API to verify identity instead of just taking your info themselves.
Any customer giving their information presumably knows they are giving said business their identity documents, the customers might not even know that the business is using Stripe's API.
Furthermore, Stripe is ostensibly coming in here to streamline the process for business taking identity info from customers. Why - in your opinion - is it worse for consumers when these-type businesses (which ask for identity), use their own-rolled id verification than using Stripe's?