Almost certainly then either (a) they were in custody at the time, which Ben Stokes isn't currently, or (b) it was for the sort of low level offences that police can authorise charge on, rather than referring to the CPS for a decision.
They can take weeks to make decisions, yes. They decide on the evidence that's presented to them, as to whether there is a reasonable chance of a successful prosecution: it's nothing to do with police advice. If they feel like there are more enquiries that could be made by the police, they'll...