One other comment in defense of Caldwell. The "big formation" he favored was part of a series of hard learned lessons that the DAF had paid a bitter price to adopt as Tactics. To successfully face the Luftwaffe (and to be real - the more elite units of the Regia Aeronautica) the DAF pilots had learned to fly in large formations and to turn into attacks from above with guns blazing, and only when and if the Bf 109s or MC 202s chose to enter a sustained engagement would they break into flights of four and pairs.
In North Africa, flying in small formations was a death sentence, because both the German and Italian fighters usually had an altitude advantage (even against Spit Vs) and seemed to routinely attack from above, and they were also typically at least a little bit faster. If they caught small groups of Allied fighters they could pick them apart, but against larger groups acting in concert they often had to break off their attacks. In the desert there was safety in numbers.
It's worth pointing out that all of these Tactics were worked out at the squadron level and filtered their way up to become doctrine - often against fairly strong resistance. So that explains some of Caldwells stubbornness.
Given that the IJ fighters were still quite often attacking from an altitude advantage in Australia it was a reasonable assumption for him to make that they would still need to use such Tactics.
What he didn't realize until after facing combat with Japanese fighters, because it had not adequately been explained in Allied briefings by then, was that the main advantage for the Allied fighters including both the P-40 and the Spit V, was speed, especially in the dive. This affected tactics developed by the 49th FG in their defense of Darwin from
March to September of 1942. 49th FG also had an experienced leader, in Lt. Col Paul Wirtsmith, and an experienced XO Major Donald Hutchinson - most of their pilots had very little experience, with 89 out of 102 pilots had no fighter training whatsoever. Training on type was similarly limited for the RAAF P-40 units as well.
49th FG developed tactics which were almost the opposite of Caldwells. Not all the IJ raids were at high altitude, but those that were posed a unique challenge. Unable to climb above the higher altitude IJ raids at 27-31,000', they had to attack from below, struggling with the P-40E's very anemic performance at that altitude, and would do so in pairs of 2 or flights of 4 aircraft, and immediately disengage by diving when attacked, then zoom climb to return to the fight. The advantage of the smaller groups of fighters was that they were able to keep up a steady stream of attacks against the bombers and thus undermined the effectiveness of the escorts - if they kept chasing P-40s another section would hone in on the bombers and starting scoring hits. This worked fairly well- they claimed 78 aircraft shot down for 19 losses, post war analysis shows the IJ forces actually lost 19 aircraft as well - 7 fighters, 12 bombers, and 1 recon plane, plus quite a few heavily damaged. The losses, particularly of bombers were too much for the Japanese and their raids tapered off for a while.
There is a good analysis of this period of fighting
here
When Caldwell took over in 1943 he apparently discounted the American tactics as someone noted above, but after the first combat they seem to have shifted over to something more like them, with hit and run attacks and smaller sections.