The biggest thing that is missing is what the the Pensacola and Northampton class light cruisers replaced - the Pennsylvania and Tennessee class armored cruisers. That is part of the reason behind their weaponry and design. The older armored cruisers were considered for refurbishment, but the newer vessels had more firepower, better range, better armor and higher speed. It was an easy choice to have them replaced. The light cruisers took over from the old armored cruisers by being able to act as a flag vessel, cruise on independent and squadron operations for far distances
The reason they became heavy cruisers was due to the LNT, but if you're analyzing their design, construction, and initial service, it's important that they were light cruisers upon commissioning and light cruisers in design.
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The US love affair with the 8" gun goes back to the 1890s, as the US always lagged behind the UK in the development of RF guns. The 6" gun on the Omaha, while a definite improvement on previous incarnations, was limited as the rate of fire of the 6"/53 in the twin mount was much worse than in the single mount. This is being discovered at the time of the WNT, so you have the US aware that their 6" mounts are much worse than foreign equivalents, and the US is going to be handicapped in the event that they accept the restriction. In comparison, the 8" gun, while slower firing, was not significantly worse that it was even with the 6"/53. In effect, the 8"/55 was seen as a superior weapon as its cumulative weight of fire would outpace what US 6"/53 guns could accomplish at the time.
As for why the US bothered putting the worse 6"/53 on the Omaha class? The US noticed that, while the ships had 8 guns, only 4 could fire in any direction at once, and as such the antiquated casemate design had to be supplemented with 6"/53 twin mounts after the fact. The rear was intended for the catapult, as noted before as well. The 6"/53 twin did have better performance than a single 6"/53, hence their use vs single pedestal mount guns.
I'll point to US Cruisers: An Illustrated Design History by Friedman. On page 112, he talks about the decision of the 8"/55 over the 6"/53. Even in his research, the initial choice for the 8" gun was almost reflexive (though I'll point out that some designs for the Omaha class also included 8" guns). It was assumed that the proposed 8"/50 would be superior due to its better range, and that there was no other argument that could be held against it. Friedman then points out that support for the 8" was not unanimous - the April 1921 General Board hearing had every single witness oppose the 8" gun (mostly on the basis that the British didn't care for the Hawkins class, that they were too expensive and too manpower-intensive, and that they were shifting to 6" guns again in the E Class.
These same supporters argued that range would rarely exceed the maximum range of the 6" guns, and as such there'd be no advantage to fight at longer ranges, and that the Chief of BuOrd and his subordinates preferred the 6" gun, arguing that [since the 8" gun was limited to 2-3 RPM at this time (the Pennsylvania class had the newest iteration of the weapon, which was approaching 20 years old by this point)], the single 6" gun would have far superior performance as they can guarantee 6-8 RPM from it.
Of course, all of these arguments were built around the false premise that they would be using single mounts. Eventually, the supporters of the 6" did relent, noting that twin mounts would perform far worse than a single mount, and the RoF would be comparable to the hypothetical 8" mount. And, of BuOrd's two projected designs (an 8 gun 8" ship or a 12 gun 6" ship), the 8" ship would project 2000 lbs per broadside vs 1200 for the 6" one.
(I'll note that this was done ~4 months after the launch of Omaha, before the vessel could be commissioned. This was a known factor)
It is noted that it's part of the reason the US relented to 8" cruiser restrictions in the LNT, as by then mounts had advanced to the point where the RoF of the 6" gun was superseding the gains made by the 8" gun. A personal observation: the 8" gun is a better investment, as the projected gains of the larger gun in future generations would be less than for the 6" gun. Even if you are to argue at the time that the 6"/53 mount would be improved over time, that means that all cruisers built with the 6"/53 in twin or more mounts in the interim would have performance significantly worse than later ships. In comparison, 8" ships lose less performance over time as the gains in RoF are far more marginal.
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Another impact that the US is dealing with is the construction of the Omaha. The stresses on the hull of the vessel were noted to be very high due to her extremely light construction.
I did find that the US considered very small cruisers in 1919 - schemes D, E, F, and H of the 1920 scout cruisers (page 113 of US Cruisers) shows the design schemes for cruisers of 5k to 6.5k in size, with either 5 6"/53 or 6 8"/50 (hypothetical 8" at the time). The latter caliber was on two of the larger design schemes. These were favored by Commander W. S. Pye of OpNav, although he thought they were too fast and wanted them reduced so that they could achieve 30 knots max (vice 33-35 of the schemes).
The US General Board "violently opposed" [page 114] this idea - because of the issues of hull stress. The US was at this time pursuing a 10k ton, 3x2 8"/50 ship capable of 35 knots with 10k nm cruise radius at 10 knots. They knew that as the Omaha had been a tight design and that the hull would be highly stressed at sea (this is a year before a single ship was launched). They were committed to relieving hull stress, which necessitated them to increase the size of the vessel, to the point where 10,000 tons was practically a necessity.
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This all doesn't even account that the US possessed different requirements than the British.
The issues that would have to be solved for the US thus have to be based around the following:
Finding adequate replacements for its aging 2nd-Rate semicapital warships on a hull for hull basis.
Making 6"/53 multigun mounts comparable with peer 8"/50 or 8"/55 multigun mounts.
Resolving US concerns about hull stress in its currently constructing vessels, of which were a well known issue.
Satisfying the requirements of the US without unduly handicapping it against other nations with less stringent requirements on range.