It varies by airline, and some can be very strict about wanting to see a card for a 3rd party booking, so it's advisable to call.

Most have a way to preapprove the charge, if you can't make it when they check in.

The issue from their perspective is that airline tickets are an easy way to turn a stolen card into cash. The thief offers "cheap tickets to Europe!", buys them with the card, and gets cash from the ticket buyer. Either the mark buying the ticket gets it cancelled, or manages to fly before the card is reported, charge reversed, and ticket cancelled.