@ aviatorhi, did you ever look outside the window in HNL? There's no other way but to turn right from 04 or 08 for that matter. Have a look at the MSA and terrain picture again, will ya.
No I never look outside.
Typically if you go missed with traffic rolling on 08R tower will ask you for heading 090 until clear of traffic then send you southbound.
You could also turn left, but there is a preference to not sent jets over the middle of the island, noise abatement I suspect.