And even in such cases when the exploitation is persistent it's still a question of how much can they get and in what time window since you might detect it and remediate the situation.
I've seen some sneaky tactics that some sites used to get details from auto complete functions of browsers, yes chrome asks you if you want to submit that data, and asks you specifically for your CC but if you mask some fields such as address and phone number (Chrome detects if it's hidden, and to some extent when its not visible due to other factors so it needs to be just cleverly disguised in rendering) when some one just auto-fills say their email and username it might also leak personal information, and if people are not too careful also they're payment data (which i believe Chrome only auto-fills on sites you visited before, and on secure connections).
I personally only have to input my CC details online every couple of months since i use PayPal or Amazon Checkout for about 90-95% of my purchases, so i rather not have my CC data stored on my machine if i can avoid it. Yes if it's compromised they can eventually get it, but it's still better than it being stored in a place where every malware on the planet knows to look for it.
If my OS or Chrome is compromised I have bigger things to worry about than my credit card number, for which charges can easily be reversed...