Stripe.js collects this data only for fraud prevention -- it helps us detect bots who try to defraud businesses that use Stripe. (CAPTCHAs use similar techniques but result in more UI friction.) Stripe.js is part of the ML stack that helps us stop literally millions of fraudulent payments per day and techniques like this help us block fraud more effectively than almost anything else on the market. Businesses that use Stripe would lose a lot more money if it didn't exist. We see this directly: some businesses don't use Stripe.js and they are often suddenly and unpleasantly surprised when attacked by sophisticated fraud rings.
If you don't want to use Stripe.js, you definitely don't have to (or you can include it only on a minimal checkout page) -- it just depends how much PCI burden and fraud risk you'd like to take on.
We will immediately clarify the ToS language that makes this ambiguous. We'll also put up a clearer page about Stripe.js's fraud prevention.
(Updated to add: further down in this thread, fillskills writes[1]: "As someone who saw this first hand, Stripe’s fraud detection really works. Fraudulent transactions went down from ~2% to under 0.5% on hundreds of thousands of transactions per month. And it very likely saved our business at a very critical phase." This is what we're aiming for (and up against) with Stripe Radar and Stripe.js, and why we work on these technologies.)
I think if it's being solely used for such security purposes, isn't shared with or sold to anyone else, and is carefully safeguarded, then it's okay. The main risk I see from it is mission creep leading to it eventually being used for other purposes, like advertising or tracking for "market research" reasons. I don't personally think it's likely Stripe would do this, though.
Responding after being caught is… good, but not as good as not needing to be caught.
Imagine I mailed you an unsolicited letter and you were legally required to burn it and never say or benefit from what was inside just because I said so. That's the insanity of these "privacy" laws.