Very common in areas where cc fraud is rampant. IME, most Asian airlines do this for online booking done directly with the airline. Note that if you book through one of the following methods, there usually is no requirement to produce the card at check-in:
--a third party travel agent (either traditional bricks and mortar, or online). Risk of fraud is shouldered by the agent, not the airline.
--in advance with the airline, in person at a staffed counter. Risk of fraud shouldered by airline but minimized since credit card and travel document (passport, ID) is presented simultaneously at transaction point.

Legal protections for buyer and merchant after the transaction takes place, are not the same elsewhere in the world as in North America or Europe, so vendors tend to be more cautious.

Usually not, and particularly if the flight is international which requires fronting up to an agent for a passport/visa check.