Yes, I think people should be able to just waltz right onto an airplane without identification. It works great for trains, why not planes? I don't see how the scenario you outlined is a security risk. There are plenty of other, better ways to make stolen tickets unusable.
How do I expect age restrictions to be enforced without ID? I don't. The US's age restrictions on alcohol are stupid and should go away.
Edit: actually, I don't see how the current regime prevents using stolen tickets in the first place. IDs are only checked at security, not when boarding. So you print out a fake boarding pass with your real name and use it to get past security, then use your stolen ticket to board the plane, where they make no effort to ensure that you are the person listed on the boarding pass you present. Easy! Well, until the real passenger shows up with a reprinted boarding pass and wonders why you're in their seat, at which point you get hauled off to jail.
How do I expect age restrictions to be enforced without ID? I don't. The US's age restrictions on alcohol are stupid and should go away.
Edit: actually, I don't see how the current regime prevents using stolen tickets in the first place. IDs are only checked at security, not when boarding. So you print out a fake boarding pass with your real name and use it to get past security, then use your stolen ticket to board the plane, where they make no effort to ensure that you are the person listed on the boarding pass you present. Easy! Well, until the real passenger shows up with a reprinted boarding pass and wonders why you're in their seat, at which point you get hauled off to jail.