If the minor child is travelling with both parents a permit from Migración is NOT
needed. It is only needed when the minor child travels with only one parent or legal guardian. When the minor child is traveling with a single parent Migración require authorization from the absent parent. If he minor child is traveling with a guardian Migración requires authorization from both parents. If one parent is deceased and the surviving parent will be travelling with the minor child the permit is also needed in addition they must have a properly legalized death certificate to obtain the permit. In all cases where a permit is needed, only one certificate ('permiso de salida para menores') is require with only one payment of the current fee (RD$2000 now). Authorization of a single or both parent can be done on one single certificate.
Minors were able to leave DR national territory without prior authorization from the parents or guardians before Decree No. 611-11
was issued. The DR is a signatory to the UN Convention on the Rights of the Child adopted of 989. Since Ley No.136-03 De la Protección y los Derechos Fundamentales de Niños, Niñas y Adolescentes doesn't directly address this and to comply with article 11 of the convention Decree No. 611-11 was issued. Section II On the procedure for granting exit permits to minors, Article 124 of the decree creates the minor child exit permit and authorizes Migración in accordance with Ley No. 285-04 (General Migration law) to grant them.
I hope this is of some use in understanding why the permit is required. Most countries that are signatory and have ratified the UN Convention on the Rights of the Child require such a permit. The USA is a signatory but has not ratified it yet and does require any an exit like DR. Canada ratified in 1991 but they have slightly different commitments.