@Linkat,
Which HGTV program are you referring to? Cuz I've never seen any show that "carefully" takes out anything.
If you're asking why, in your particular case, the chimney brick wasn't re-used, the simple answer is cost. Breaking down a chimney is easy, removing mortar from brick isn't. It's time consuming. A Journeyman brick layer would laugh at you, a laborer would say they don't get paid to break rocks all day. Chiseling mortal off used brick is just not going to happen in most professional settings.
Now if you, as the consumer, wanted to... Which why didn't YOU take the brick for a DIY project?