A few obvious reasons for a dirty dive, as opposed to a clean dive.
- It is lower in airspeed, so you won't need to get rid of that airspeed to land.
- It puts the gear down early, before the fire buggers up the hydraulics and/or electrics.
- It does get rid of height quickly, and you'd rather be on the ground on fire, than airborne on fire.
Incidentally, I personally think it's a silly bit of the CPL to a large extent. I don't disagree with it's inclusion, but many of the far more likely emergencies - comms failure, generator failure, control restriction, fumes in the cockpit - get pretty much ignored in favour of the "big two" of engine fire and engine failure which are astoundingly rare by comparison with those.
However it's in the test, learn it and do it that way!
G