The main reason that you would want to record a declaration of unlawful assembly (if you are the police) is so that you can document that the declaration was done properly and that the people who were participating in the assembly were treated right.
An assembly is unlawful if either one of two conditions applies. First, it is unlawful if the gathering is happening for some illegal purpose. Second, it is unlawful if the people are doing something legal but are doing so in a way that creates too much of a disturbance. When an unlawful assembly is declared, the police must do so very clearly. They must do so in a way that everyone can hear. They must do so multiple times so that it is even more certain that everyone is aware of the declaration. They must allow demonstrators enough time to disperse and must give them ways to do so.
Police can prove that they have done all of these things if they record their declaration of unlawful assembly. That will make it clear if they have made the announcement loudly and multiple times. It will make it clear if they have given the protestors adequate time and means to break up their unlawful assembly. For these reasons, it is a good idea to record a declaration of unlawful assembly.