General audiences go to see movies all the time with characters they don't know. I think the only reason to not create a new crew, is to gain support of the base. But I don't think the base would care either way. They'll either like it or not. Just like they like or don't like having Kirk and crew.
"The base" will show up for any Star Trek film. The general audience is more likely to show for a movie with Kirk and Spock, because those are the characters associated with Star Trek.