The travel consent letter is addressed to immigration officers, who want to avoid that one parent kidnaps the child to another country without consent from the other parent, thus making it very hard to retrieve the child.
Traveling inside the country is much less of a risk, since there is no issue of lack of extradition treaties domestically. Also, as there are no domestic immigration checks in the US (unlike, e.g. in China), it is logistically much more difficult to catch domestic kidnapping - the TSA doesn't even require children to show IDs for example, though your airline may still want to see some kind of ID, such as a birth certificate, or a passport.
Note: A travel consent form can potentially be useful for domestic travel if you do not share a last name with the child to demonstrate that you're related in case of hospitalization at the travel destination.