We have an interpreter. Why Add Captions?

Our church already has sign language interpreting, why add captions?
www.robson.org/capfaq/online.html#VoiceRecognition writes:

Captioners and sign interpreters address two different groups of people.

Prelingually deaf (or culturally Deaf) people have sign language (usually ASL) as their first language. English came later. They will be much more comfortable with an interpreter, and their comprehension level will be higher. For someone accustomed to ASL, English is quite limited in its expression, and written English is very "dry." Additionally, a Deaf person who has spent most of their life communicating in ASL may not have developed the reading speed necessary to follow captions in realtime.

Postlingually deaf people (or late-deafened adults) learned English before they learned to sign, if they learned to sign at all. For these people, captions will provide a far greater comprehension level. Of the deaf and hard of hearing population in the United States, roughly 10% actually know sign language. Captions benefit the rest.

Each method of communication has its strengths. For example, in a speech with heavy use of proper names and specialty terminology, it may be easier to follow captions than a frantically fingerspelling sign interpreter.

The maximum flow of information and comprehension will occur when sign interpreters and captioners work together at the event.