Absolutely false. From the proposed regulationAlso significant to point out that Southwest is exempt from the proposed DOT regulations as they don't have assigned seating.
If an airline does not provide advance seat assignments at booking at no additional cost for those traveling with a young child or has an open seating policy, the airline should have a policy and procedures in place to ensure adults traveling with young children are able to be seated so that at least one accompanying adult is adjacent to each young child at no additional cost. For example, an airline with an open seating policy may permit an adult traveling with young children to board early enough in the process to obtain adjacent seats. In the alternative, an airline might choose to block seats for use by these travelers at no additional cost.