…...However, suppose they'd survived, what offensive role could they have played in the Far East?
OK, suppose Phillips decided not to sortie without air-cover, and the Buffalos of 435Sq RAAF and 488Sq RNZAF have an early Christmas amongst the unescorted Japanese level- and torpedo-bombers. Remember, the Japanese bombers were all low on fuel when the made their attacks, attacked in several small waves, and none above 11,500ft, so even the Buffalos would have been able to shoot them down or drive them off. Then Force Z scarpers back to Singapore intact.
At that point, it's highly likely they would have been withdrawn from Singapore pretty soon after, either to Ceylon or Darwin. One option is to consider what would have happened in the defence of Java if Phillips and Force Z are still around. Instead of the Battle of the Java Sea being fought by a mix of Allied cruisers under Dutch command, we'd have a battleship and a battlecruiser to add to the party. If
HMS Hermes has been attached then we also have some carrier support, though it's more likely that
HMS Indomitable would have joined Force Z by then, as originally planned.
That also makes it unlikely that the Dutch Admiral Doorman would have been leading the ABDA Command cruisers into action. Doorman had no naval combat experience and made a series of bad decisions in assuming what the Japanese would do. The USN's 59th Destroyer Division won at the Battle of Balikpapan because they acted under US orders
without the distraction of the ABDACOM structure/interference.
So we have
Indomitable's Sea Hurricanes for air-cover during the Battle of Makassar Strait, preventing the cruiser fleet being forced to retreat, leading to the Japanese invasion force being attacked by a fleet with two big-gun ships plus torpedo-bombers form
Indomitable. The presence of Force Z would have given the Japanese a headache as they were still busy defeating the Americans in the Philippines.
If the IJN are held off Java then there is no invasion of New Guinea, no subsequent attacks on Darwin, and thus Darwin remains an effective naval base. Better resupply to the Dutch East Indies is possible and, instead of sending P-40s to Australia, the USAAF sends P-40s to help the Dutch. P-40s with Hurricane II top-cover would have been a much better defence against the IJN's Zeros.
Even if they do little more than delay the Japanese on Java for a few months, come May we have the Battle of the Coral Sea possibly replaced by the Second Battle of the Java Sea, as the Japanese try to bring their carrier fleet to bear on the Java problem. The USN would still be able to break the code protecting the Japanese radio orders and could send their Task Force 11 carriers (which only had cruisers in support), now with Force Z's big-gun support plus
Indomitable, to attack the IJN carriers and mop up the Japanese transports.
So, yes, it is possible to theorise a quite big part for Force Z if Phillips had accepted air-cover.