Assuming Amazon's endgame is optional integration with their payment/delivery platforms, there's certainly the hypothetical possibility of accidentally purchasing from confusingly designed sites you'd never give your cc details to though.
Since chargebacks - unlike social spam - cost money, Amazon has every reason to be more cautious about their permissions and confirmation screens, but the wary user probably isn't unjustified in hesitating when asked to sign up for a free service using a login they normally use to buy stuff with.
But might you now have to put up with Amazon targeting even more ads and recommended products to you based on the various sites you've logged into using their service? :/
My complaint is the payment for the login service through the use of my behavioral data I'd rather keep private. I have never clicked through an ad to purchase anything. I dislike seeing ads that are clearly based on my behavior but don't understand the intent of that behavior (i.e. showing me ads for generators because I looked at a few on Amazon to compare the stats to the one I already own). I also dislike seeing ads in general because they are not a useful feature to me. I'd prefer to pay for features in a more direct and favorable (to me) manner. I also dislike the concept that targeted ads are in some cases specifically designed to influence my attitude toward brands and provide me with information that may not be absolutely true but which they will hope I internalize to influence my future purchasing decisions.
Obviously, this is my personal preference, and I do understand that ads can be a useful revenue stream for companies targeting other users with different profiles from mine.
I'll finally start using "Log on with" if I can use Amazon.