So your first point, on ships "fast enough to dodge shells" is VERY dubious to the point of tragedy essentially.

The line of thinking, that speed is your armor, had been tragically done away with in most respects when naval thinkers looked back on the performance of the RN's battlecruisers in WW1. As soon as you meet a ship with similarly sized guns that you have to fight, or worse yet is as fast as you your lack of armor is a very real, very fatal problem. Dodging doesn't really change much, when you consider that even a hit rate of say 10-15% was considered AMAZING, battles such as Jutland routinely featured hit rates of 5% and even lower by certain ships, so this was the environment that navies were operating in, radar fire control was still just an idea and even then not perfect. While central director control and manual computers were still vulnerable to conditions and human failings.

And under the treaty very few capital ships were built, fewer than 20 worldwide before the system broke down. What the USN and most nations built lots of, was modern cruisers to fill out their tonnage quotas and replace the out of date protected cruisers and early light cruisers of WW1 vintage. Under the original Washington Treaty, cruisers were limited to 10k tonnes with no guns larger than 8in.

Thus on the Treaty Cruiser Classes such as the Pensacola onwards. Very quickly it was decided that a 10k ton cruiser couldn't be all things to all people. And the heavy 8in guns, long range, and ability to serve as flagships and part of a task force operating at high speed were all initially decided on in favor of thicker armor. However the Pensacola's came in rather underweight, and in each succeeding cruiser design more weight was dedicated to armor, from the Northampton's, the Portland's, to the New Orleans class. By the New Orleans class finally the cruiser's armor at least on the turret barbette was designed to be thick enough to defeat other 8in shells. Comparing the Pensacola to the New Orleans we see a full inch of maximum belt armor on the side of the ship and .5in of additional deck armor protecting the ship from shells and bombs dropping vertically.

From the NO's virtually all other classes of cruisers for the USN in WW2 would evolve. A parallel efforts to use the lessons learned but in a 6in armed light cruiser would result in the Brooklyn class, whose hull would then be modified into the Wichita class CA and serve as the base for all follow on CA and CL classes. One of the Brooklyn's that survived the war actually was transferred to the Argentine Navy and was sunk in 1982 during the Falklands war as the General Belgrano.

But we should also consider what battleships were built, and in particular something called the "Escalator Clause". Under the Washington treaty no new ships could be built with any guns larger than 16in. This was planned to be reduced to 14in in the London scheme, but incase a signatory (Japan and Italy basically) refused to agree it would revert to 16in. The USN and RN both began working on new battleships with 14in guns. The RN's King George V class was eventually built as designed with 14in guns for a number of reasons. However thanks to some additional foresight and industrial capability the USN's North Carolina class would go from 12X14in guns to 9X16in guns, setting the standard for the following South Dakota and then Iowa class.

In general though the nation that absolutely made violating the terms and spirit of the treaty a fact of life was the IJN. Their new cruisers through the 20's and 30's routinely were overweight and in the instance of one class the Mogami's were built with 6in guns, with features included and the understanding that as soon as they could be would be replaced with 8in guns and become CA's.