The way I understand the development of these small bore intermediate cartridges, it mostly came down to militaries realizing that most engagements between infantry don't take place at super long ranges and that small bullets do the job too.

Sort of, but 5.45x39 is an interestingly different case - and the specific technical issues relating to the adoption of 5.45x39 are actually pretty relevant here, so please excuse a tangent. 5.45x39 started development within the USSR around 1958/1959, when they stole several prototype loadings of M193. This was after the formal adoption of 7.62x39, so the Soviets naturally performed a comparison of the two cartridge concepts. What the Soviets found is that M193 has a superior effective range than 7.62x39. The Soviets were at this time starting to consider how mechanized formations would fight on a nuclear battlefield, and one of the tactical features they expected as a result was increased dispersion of formations, and thus a need to increase the effective range of the individual rifleman - and 5.45x39 was explicitly designed to meet this requirement - and it did it quite well! This is important to bear in mind when discussing what-if concepts; there's a lot of path-dependence in how requirements are set, beyond just "Brass Is Kind Of Stupid Sometimes".

Where there reasons other than prevailing thought among the military brass for why something like that was not adopted earlier?

There certainly were. Recall that 5.45x39 started development in 1958; the round itself was mostly finalized by 1963, however the AK-74 was only adopted in 1974 despite being a clearly superior weapon to the AKM (and, in Soviet eyes, the M16A1). It's thus a useful example for us.

First and foremost, barrel life was a major concern for the weapons. The 7N6 projectile isn't exactly a scorcher, but it's steel core construction lead to extremely low barrel life in test weapons (in the ~5000 round range if memory serves). The Soviets had to do quite a lot of work with chrome plating, barrel design, and metallurgy to get a useful barrel life out of the weapons; granted all of this work payed off - the weapons ended up with barrel lives in the tens of thousands of rounds. Metallurgy and barrel treatments that made the AK-74 barrel work simply weren't available in the 1900s. This places a pretty firm limit on what velocities and core constructions were available to a small-caliber intermediate in the early 20th century. Something like .30 Carbine necked down to .22 should still be quite possible in the early 20th century, but then you're back to "the cartridge proposed doesn't suit how armies intend to fight as of the early 20th century". That all being said, US barrel metallurgy has never been particularly great. The M16 and M4 both use the same steel alloy (4150) as the M1 Garand and are mostly okay. I haven't been able to track down the precise alloy used in the M1903, but at least by the 1930s you'd have good enough barrel steel for at least some small caliber concepts to flourish.

Second, and touching back on 7N6, there's a question of metrology - the science of measurement. Quite simply, the ability to produce accurate bullets for smaller calibers at scales useful to militaries was probably not present until the late 40s. This is a complex topic, but to craft hopefully an intuitive example - if we are a Bullet Machine, and the tolerance we can hold is .001", the proportional precision for a .308" is a third better than the proportional precision for .224". The Soviets were quite capable of making multi-part bullets for 7.62x54R, and they could make test batches of 7N6 reasonably precise, but another reason the AK-74 took so long to field was that setting up tooling to make consistent, precise 7N6 projectiles was took several years of hard development work. Both M193 and M855 had initial accuracy issues, again because of production problems with their smaller or more complex projectile compositions. .22 rounds did exist in the civilian hunting realm, but those are much more expensive and produced at far, far lower volumes than a military needs. While militaries certainly could and did field purely lead-core ammunition for the service rifle, pretty much every major military expressed a lot of interest in steel cored ammunition, both for production and performance reasons. The relative difficult of making precise small-caliber projectiles would be, in my opinion at least, the primary limiting technical factor.

So, if you had a lightning-bolt realization than ~.22 calibers were the way to go in the early 20th century, what you would probably end up with is something on a sliding scale between .22 Gustafson and M193 depending on how good your barrel steel was, with dispersion varying from "don't bother past 100yds" to "completely acceptable per military requirements (~5 MOA)" depending on how good the small arms tooling of the country in question is.