There is a lot more in play if you look at the big picture. The Government is more than happy to miss out on the VAT via a process that ensures that those transactions are properly recorded as on balance sheet and payment procedures are done with plastic rather than cash. The cost of VAT is more than offset by the other taxes (not only at the Federal Level but also City Taxes are very relevant) that are collected because for this scheme to work, the issuance of formal tax invoices must happen.
Credit cards are a blessing for the Tax Authorities, as everything credit card related leaves very easily traceable information. Visitors come loaded with plastic, and despite the odd bargain hunting type that may still want to try the cash route, the overall balance will still be very positive (and lucrative) for the Government and AFIP. Also, Argentina is looking to be perceived as offering the same advantages as neighboring countries that have similar schemes in place. I think it can be expected that initial program participation will be small and cautious, but as the system is rolled out in full and the Federal Tourism Authority starts strong campaigns to advertise this benefit, more and more lodging providers will be persuaded to join.