After the turn of '42 Halsey could field Saratoga and escorts--mostly those destroyers in short supply--while he by necessity relied on the three Sangamons in the Pacific as oilers themselves. Or he could field the battleships but rarely chose to work with both at the same time and then mostly by placing the battleships on training sorties, not operations.
In addition, the older battleships were hobbled by a lack of anti-aircraft armament and required modifications to their internal subdivision which was accomplished--if I'm not mistaken--in the Noumea/Efate area by spring '43 although I believe armament mods were managed largely at Pearl Harbor. The battleships also sufficed as oil supply depots while they swung at anchor...not a new concept or practice as the prewar buildup at Pearl attests.
Until the issues of fuel, armament and escorts were addressed--and this began to really kick in in November of '42--Halsey and SoPac were not operating with the overwhelming force desired of the offensive. By spring '43 the handwriting was on the wall.
Yet, even as late as November '43 the dearth of hulls, if not fuel, made itself felt as Halsey sent the carriers up to raid Rabaul on the 5th and the 11th with minimal escorts (although the plan as early as the beginning of the year was to restrict cruiser escort employment to the Atlantas) although this does reflect the overwhelming emphasis on the invasion of the Gilberts in the Central Pacific.
On the other hand, the Japanese were in decline during this same period for those same reasons: a shattering of their formations, their strength and their ability to project such forces as they had. They began the campaign on a seesaw more or less to their advantage with their strength at its height but quickly lost every advantage as resources and infrastructure for the Allies not only kicked in but swamped the Japanese. The comment by one Japanese staff officer as related in Japanese Destroyer Captain (Part 4, Section 5) that it was the Japanese, not the Americans, who were being bled white speaks volumes...they knew.
An evaluation of infrastructure and bases each antagonist relied upon is very interesting: the Allies had in-theater bases such as Efate and Noumea--to name but two--while the Japanese relied upon precisely one with anything like supporting facilities.
Others may check further on this but I believe Rabaul didn't even possess a wharf of consequence worthy of the name; the Japanese relied very heavily on temporary accommodations wherever they went in the Solomons and never had the ability to provide resources or equipment on a mass scale.
The Japanese really had no right to wage war in the '40's; but that's what unrepentant militarism and arrogance can purchase for a nation.