Just checked the Washington treaty.
Capital ships were allowed to add up to 3000 tons as part of a refit, but not change calibre or number of main guns, or side armour.
So cruisers can't use that to add armour as a) they aren't capital ships and b) it's armour.
So you would need a different treaty to build cruisers that were designed for retro-fit of armour.
Butterflying the Hawkins class, or agreeing to scrap, and restricting to 6" guns and 8,000 tons in the treaty works better in the long run for the RN, and stands a good chance of being agreeable to most parties.
Except nobody on the naval side in the RN delegation saw that.
As Beatty was 1st sea lord, and according to his bio was "responsible for negotiating the washington naval treaty" that shouldn't be too surprising.
The French and Italians stopped building 10000 tons 8" cruisers, and went to 8000 ton 6" as soon as the London treaty was signed in 1930.
So probably not a problem for them.
The Japanese were building 5,500 ton (ish) 5.5" cruisers until they felt the need to counter the Hawkins.
The Furutaka and Aoba classes were 8,000 ton, not 10,000 (and laid down post Washington). So no 10,000 tonners until post Washington.
Agreeing to an 8000 ton limit, and doing a minor redesign to take 5.5s or 6" rather than 8" before even laying the ships down makes these ships as good as anything in the world.
The US were building the Omahas (8,000 ton, 6") at the time of the Washington treaty, which they presumably thought were satisfactory, or they would be building bigger and heavier armed. I don't think the problems with the Omahas were due mostly to size.
The US hadn't built any cruisers for a while, and they weren't particularly well designed, with an old-fashioned look to them.
Double banked casemate guns, in 1920?
With a restriction to 8000 tons and 6" guns I'm sure the next generation of cruisers would have been better.
Probably like the Pensacola class, only smaller, as the 6" guns allow for weight savings not only on the guns but also throughout the ship to maintain roughly the same performance, but with lighter guns and armament.
Agreeing to 8000 tons and 6" puts the Omahas at the top end of cruisers, rather than instantly obsolescent when everyone starts building 10000 tons with 8".
From the viewpoint of 1921/22, and absent the Hawkins class, the lower limit on tonnage and gun size makes sense for everybody, particularly in the context of an arms (and cost) limitation treaty.