That day -- and over the week since then -- we had several long internal discussions about it. We've decided to go ahead and add the ability to disable it. This is now documented at [2].
We want Checkout to be simple, and we didn't want to add too much customization since doing so would go against the grain of the product. The whole point of Checkout is to provide a merchant with the right defaults and to improve over time. But we decided that Remember Me is a special case because there's the appearance of potentially misaligned incentives: someone could argue that Remember Me exists for Stripe's benefit and at the merchant's expense.
This is exactly the opposite of what we're trying to do -- the goal is to increase conversions for businesses using Checkout and to get better at doing that over time. But we're adding the opt out to emphasize that we're not trying to force anything.
If you do disable the checkbox, users who stored their accounts elsewhere will still be able to pay on your site in a single click. (This seemed like the most merchant-friendly option to us -- this way, you can still take advantage of the network.)
Thanks for all the feedback!