Why would 3D-Secure work better in Europe than in the United States? I fail to understand that from reading your comment.
Yes, it requires extra authentication (My issuing bank has chosen password as the auth - some others use the bank code boxes for One Time Tokens). All online stores that I routinely buy from in Sweden and in Europe have 3D-Secure turned on. The only exception I've encountered is an airline.
The customers don't get to choose - it's not optional for customers. It's optional for merchants/shops. If they however disable 3D-Secure: They're liable though.
It requires the use of a password, and adds additional steps to the checkout process. You can't really make it mandatory on your store, as conversions/sales would crumble. So, you make it optional.
If it's optional, only the most security conscious customers end up using it. Those are the customers with the lowest risk of having their card info stolen, and the most likely to report it quickly if the info is stolen.
So it adds more protection around a tiny fraction of your sales...the sales that were already very unlikely to be fraudulent.
It doesn't make any notable change to "the cost of online fraud in the US is 100% on the merchant/seller".