Why didn't Phoebe become an intern for Winston?

Am I missing something completely? Phoebe gets mad that she can't be a ghostbuster, then the gang finds out 10 minutes later there is an entire paranormal research center and no one suggests Phoebe participate in some capacity? Am I missing something?

Edit: Granted I get that the rest of the movie happens pretty quickly after, it just seems odd it never came up as a part of dialogue prior to everything going haywire.

Edit 2: Changed some stuff for clarification of the actual point to avoid folks missing the point of the post.