Given the way Stripe has implemented this today, Stripe might as well be selling their business customers a <input type="file" /> tag for Driver's Licenses, because that's the level of security 99% of all business will be using around this. There's going to be Amazon S3 buckets filled up with Drivers Licenses JPEG's provided by Stripe Identity, in a few months time.
What makes you think these don't already exist? Have you ever needed provide your identity information to use a service online (e.g. a insurance service, bank, alcohol/weed delivery, crypto market, etc.)? Where do you think the identity information you provided is stored?
If you don't use these type of services, then nothing will change--stripe won't magically have all your identity info. If you do use these services maybe they'll partner with Stripe, maybe not. The only outcome I can see from this news is that it's likely there will be fewer AWS buckets with your identity info moving forward, because Stripe can do that for you now.
Isn’t that already true for businesses that store this data from any source?