As part of EMV, the liability is typically shifted to the merchant for non-EMV authenticated transactions. This provides strong motivation for merchants to do a better job of filtering out fishy transactions.
The only solutions I've seen to using EMV itself for online/phone transactions involve having a more advanced card (i.e. with LCD token readout) or a standalone card reader to interact with the chip.
Merchants already have to pay back the transaction, plus a charge, plus we're out the merchandise. We already have plenty of incentive to spot fraudulent transactions.
