So Signifyd seems to be a set of statistical methods to find unusual activity - "We combine your ... data with our datasources and turn it into a easy-to-interpret score and behaviorial signature." Their website doesn't restrict application to eCommerce. Indeed, the idea is very general and could just as easily be applied to electricity/water theft, tax evasion, and other areas.
By formalizing the analysis, it's much more reliable. Instead of "Hey, that dude has a lot of returns", you should get something much more useful: "User 12341 has a problem score of 92%. He reported failed delivery for 19 out of the last 25 orders. There is a 0.001 probability of that happening by chance, therefore we should investigate in more detail".
Finally, there are other types of "bad" transactions that don't require stolen Credit Cards, but can be detected with good data analysis:
Buy something and re-sell it. Put a bag of sand of identical weight into the original packaging, re-seal it with a shrink-wrap machine, and return it to the retailer (this also works at physical stores). The retailer cannot defeat this without inspecting every single returned item.
Buy something and re-sell it. Claim it wasn't delivered and request a refund, or a replacement product. As many online stores try and keep customers happy, often a replacement will be sent, or a refund offered even if there is proof of delivery.
Find a broken product (e.g. Dumpster diving or eBay). Find a store that sells said product and buy it. Sell the working product that you just bought, "return" the broken product to the seller and request a refund.
So the reason we need fraud-detection methods is because fraud will occur even if the payment system is perfect (and it isn't).