Everything I have read indicates (if not outright states) that the 8" 10000 ton limit was derived from the Hawkins/Frobisher, which in turn came from the Atlantic cruiser, which was evolved from (or as a replacement for) the Towns. Designs and intentions to design by other navies were as a counter.
I am stretching my memory a bit here and will have to reread what I have on the Atlantic cruiser concept, but I believe that its origin was in a belief that Germany was building something of that ilk that needed to be countered.
Anyway, long story short, the Hawkins/Frobishers were not really that successful and battle cruisers were hideously expensive; it is doubtful that, even if built, the WNT style cruiser, as you have said, would not have lasted long, something bigger was needed and many something smaller were needed too. In fact, naval design being what it is, once everything that was required was incorporated, none of them would have been anywhere near as light as 10000 tons.
The Hawkins-class was unsuccessful mostly because it was woefully outdated, between the mixed-firing powerplant and the hand-swung pedestal mounts. A fully modern ship with oil firing and powered, enclosed mounts proved much more successful.
As for the 8" 10,000-ton limit being derived from the Hawkins class, yes, but actually no. Certainly the USN move to 8" was motivated very heavily by the Hawkins-class, which in turn motivated the British to move to 8" to match what the USN was doing. However, per Friedman the contemporary
French move to a 10,000-ton 8" cruiser was motivated by what the Germans might build under Versailles restrictions, and the Japanese Furutakas were motivated entirely to outdo the
Omaha-class in scouting action - and while it took a while for the details to come out on them, the Furutakas are mentioned as another factor driving development of the 10,000-ton 8" cruiser.
Even then, the Hawkins-class was only part of the calculus for the USN. The arguments of the effectiveness of 6" versus 8" guns in open-water action made by Dreyer below were repeated in the USN[sup]1[/sup], and both the USN and RN found that the combination of speed and range they wanted mandated a very large ship anyway.
Regarding larger ships, well, the USN did look at
a 12,000-ton ship in their 1919 and 1921 studies. This was the opinion on it:
While providing desired capabilities, this design was considered too large to be affordable.
Fundamentally, heading into the early 1920s
everyone needs cruisers en masse, and generally they need cruisers operating deep into the ocean away from basing, whether for trade protection or scouting; fleet roles were mostly covered by WW1-built ships. This mandates a large ship, that much is clear from the design studies of the period, just for the required speed and endurance - but it also demands affordability due to the sheer numbers involved.
You would get larger 8" cruisers later on as numbers get filled, the fleets get experience with the 10,000-tonners, and
someone (probably Japan) escalates matters, but there's going to be a very large initial generation that is basically just the 10,000-ton Washington type.
Pre WNT the RN was looking to an evolved Courageous-style large light cruiser, that carried multiple aircraft and possibly even torpedo boats for the China Station in particular. WNT led them to switch to a planned force of WNT cruisers instead.
They were looking at this type of cruiser, but this was in addition to various 8" cruiser designs up to 10,000 tons. The Courageous-type large light cruiser, though, was probably not going to happen on cost grounds - despite attempts to keep them at 15,000 tons the RN was horrified to find they would be at 19,000 tons.
The following, per Friedman, was the outcome of design studies in 1920-1921:
On this basis, Dreyer suggested five alternatives:
A: 10,000 tons, 31 knots, eight 8" in twin splinter-proof
B: 8500 tons, 32 knots, five 8"
C: 7500 tons, 35 knots, four 8"
D: 7500 tons, 32 knots four 8"
E: 7500 tons, 25 knots, four 8"
Design A would counter the projected US 10,000-ton cruisers, if British finances permitted. It would not be desireable to go below 7500 tons, 'as this would is the smallest size now advocated by other countries'. ... No 6" cruiser could effectively fight an 8" cruiser. Dreyer preferred a 7500-tonner with four centerline 8" guns.
...
DCNS agreed that any new trade protection light cruisers would have to be armed with (at least) 7.5" guns, and would probably be comparable to the big Hawkins type. He doubted that a ship of smaller displacement could combine sufficient radius of action and armament.
More detailed DNC design studies reached similar conclusions to the USN vis a vis the effects of speed and endurance requirements, namely that it was going to be a struggle to fit everything desired into even 10,000 tons.
- Note that the relative merits of the two guns were very different from what they were even by 1930 - for one, this was still before effective powered mounts for 6" guns, and an enclosed turret for a 6" gun had very real rate of fire penalties.