These virtual cards are not very reliable and are not to be trusted unless issued by a bank, somewhat ironically. They can only work in certain regions for a limited time and are not always accepted by all vendors.
Some exchanges are offering cards of their own (I think Bitstamp has this service) or withdrawals to cards. However, if being identified is a concern, this won't work for you. The best thing you could do is get a localbitcoins cash transaction, buy a prepaid card, and load it up with that cash. Otherwise, you don't have many options.
From my experience, the Virtual card worked for me as good as the plastic one. It is not accepted by all vendors, indeed, but it's accepted by most of them.
In the privacy matter, however, you are indeed correct. These cards have extremely low "lifetime" limits (I think that's some 250 EUR total lifetime top up) if you want to use them without being verified, since they comply to EU regulations on the matter. If you want to stay anonymous, I guess that face to face transactions to cash are the way, but I find them way to risky for the average Joe.