I would think it would be easy to flag a new account either by birthday or name both of which you need to travel. It wouldn't surprise me in the least to learn that they have a list of people and their identifiers who have been terminated to avoid this very situation.
I am sure it is routine to bounce all fields of new accounts against terminated accounts. If anything matches, then flag the match and get an experienced human being to look at the two accounts (new and terminated) in detail. That's where you find amateur attempts to beat the system. ("Joe Blow" in one account, "Joseph Blow" in the other.)
Once a human beings starts looking at the records, the cheater is toast.
I do this kind of thing for a living, but not at an airline.