^^ That's not necessarily a problem. There's nothing wrong with stylized writing or pseudo-Socratic dialogue. If it's done well. People like Serling and JMS do it well. Others, like Chris Claremont, do not.
I'm dubious about the idea of recreating Serling, either through re-use of old recordings or CGI and mimicry-- that would be too gimmicky at this point since it still couldn't be done photorealistically. Although I think it would be fine to re-use his opening narrations in the title sequence.
The best thing about Twilight Zone: The Movie
(along with the prologue) was that they used Burgess Meredith as narrator, since he had a strong history with TZ. I don't think there's anyone around now who could fill that role. Bryan Singer may be the producer on the new show, but he's still following in Serling's footsteps. If he has the proper screen presence, he'd be fine, but any other host who can deliver the proper ambiance would do just as well.