I can provide some engineering context for why magazine capacities were what they were, although this may not specifically answer what you're looking for.

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While any soldier is always going to wish that they didn't have to worry about reloading, it's important to understand the context of these rifles. For the most part, the semi-automatic rifles that were in development at the end of the interwar period and into WW2 were designed with a magazine capacity higher than that of the bolt-action rifles they intended to replace. Major outliers existed in the form of the French MAS-40 (with the same 5-round magazine of the MAS-36) and the Belgian SLEM/EXP-1 experiments by FN engineers in Britain that also used a 5-round fixed magazine. However, even these outliers would come up to the 10-round "standard" when they matured postwar into the MAS-44 and FN-49, respectively. So the added firepower afforded by the comparatively larger magazines was appreciated by decision makers of the time, especially when compared to the 5-round magazines they'd generally be going up against.

A broad look at magazine development of the time can explain a lot behind the reasoning for the selection of a 10-round magazine. When nations first started adopting modern smokeless-powder rifles in the late 1800s, magazine design and capacity was a major design issue. The Lee-Enfield stands out among its contemporaries for its semi-detachable 10-round magazine, while most competitors instead stuck with 5-round magazines. The Mauser system, which was by far the most successful of the era, would come to use a 5-round fixed magazine that sat flush with the bottom of the stock. While the magazine capacity may have been half that of the Enfield system (and less than other rifles like the Lebel or Carcano), the flush-fitting Mauser magazines were more durable and better protected from impact, reducing issues relating to damaged magazines. The Enfield's detachable magazine seems like a great idea on the surface, but the reality of it was far from what one might expect - magazines were expensive and not exactly interchangeable. In fact, the Enfield magazine was intended to be chained to the action and only detachable so that the user could unload the magazine.

Going forward into the interwar years when self-loading rifle development began to pick up, magazines again became a major issue. The Garand's staggered-feed en-bloc clip offered benefits similar to the Mauser system - namely the study, flush-fit magazine - and combined it with a faster means of feeding the rifle compared to the stripper clips that contemporaries used. The Soviet self-loading rifle experiments experimented with magazine capacities as high as 15 rounds (AVS-38) but ultimately standardized on 10 round magazines. The Soviets went what sounded like the more intuitive route and used detachable magazines, but they ran into a problem that would be common in many other guns of the time - magazines were expensive and rarely as interchangeable as one would hope. As would be the standard for most contemporary self-loading service rifles developed at the time, the magazines weren't swapped out, but rather fed via the same 5-round stripper clips used by the bolt-action rifles. German experiments followed a similar trend, with even the nominally-detachable magazine of the G43 being fed by stripper clips in practice.

A lot of the same design drivers of bolt-action rifles would come into play with the decision to standardize on 10 rounds. Large magazines protruded below the action and were vulnerable to damage. Magazines were fixed either by design or doctrine due to the greater reliability of fixed magazines, cost of producing large numbers of detachable magazines, and inconsistent interchangeability of magazines. And with magazines fixed and fed in combat via stripper clips, 10 rounds starts to be the upper limit of usefulness before it becomes difficult to feed the magazine. And if the magazine is only being fed in 5-round increments anyways, the long-term fire rate isn't necessarily improved by the jump from a 10 to 20 round magazine.

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A look at the NATO Light Rifle Trials postwar shows just how ingrained this distrust of magazines was. Both the M-14 and FN FAL were developed with the idea of feeding them using stripper clips despite their relatively reliable detachable magazine system. Magazines up to 30 rounds were designed for the FAL, but even the 20-round magazines were found during trials to have problems relating to weight, expense, and bulk that stripper clips avoided. And the magazine capacity of the M-14 and the FAL came from wishes to replace both the Garand and BAR with a common platform. Even across the pond in the USSR, they had adopted the SKS with a 10-round fixed magazine after WW2. The AK-47 was initially deployed as a "submachinegun," and it wasn't until several years later that Soviet authorities had decided to adopt the AK-47 as a standard service rifle.

I can speak only about the SVT, but the desire for more ammunition was present since the beginning of production, even before the war. The precursor to the SVT, the AVS, had 10, 15, and 20 round magazines.

However, there were issues. The rimmed nature of the 7.62x54r rifle cartridge makes creating high capacity magazines complicated, which is why the DT had such a complicated pan magazine. Extended magazines showed issues, which is why the SVT was produced with 10 round magazines, which allowed the rifle to strike a good balance between reliability and high capacity.

Once the Great Patriotic War began, the SVT proved far from an ideal choice for the war. Soviet era historiography made the excuse that the rifles were just too complex for a conscript to take care of properly, but the actual answer was that manufacturing quality took a nosedive when production had to be expanded. As a result, the average rifleman was stuck with the old Mosin rifle. The SVT did find a new niche. Since the Red Army was experiencing a shortage of automatic weapons, many units were converting their SVTs into full auto rifles to supplement light machine guns. As a result, the SVT was turned into the AVT select fire rifle. Naturally 10 rounds is not nearly enough for a select fire weapon, so efforts were made to develop high capacity magazines. The official manual describes a 15 round magazine, some sources say that 20 round magazines were also developed. The development of a high capacity (exact number not given) fixed magazine for the SVT was also requested in 1943.

Sources:

http://tankarchives.blogspot.com/2019/12/artillery-wishlist.html

http://tankarchives.blogspot.com/2018/01/full-auto-svt.html

https://warspot.ru/3331-ya-budu-rabotat-poka-dyshu-k-dnyu-rozhdeniya-f-v-tokareva

7,62mm samozaryadnaya vintovka obr. 1940 g i 7,62mm samozaryadnaya snayperskaya vintovka obr. 1940 g. Rukovodstvo sluzhby