Those .30 caliber bullets were being propelled by smokeless powder at much higher velocities than those .45 caliber and 11 mm bullets propelled by black powder. To take the US Army cartridges, 30-40 Krag vs 45-70 Gv't, the smaller 30 cal. would be going around 2400 feet per second, as opposed to around 1500 feet per second for the .45 bullets, have 2300 ft pounds of energy as opposed to around 1600 ft lbs of energy . That higher velocity and greater energy meant it'd go further- accurate shooting at long range with a big black powder cartridge like 45-70 was difficult: at 200 yards the bullet would drop around 18 inches, as opposed to around 3 inches for 30-40 Krag. Going to lighter bullets meant that ammunition didn't weigh as much, and more rounds could be carried per soldier, or per supply ship. Smokeless powder also meant that guns didn't need to be cleaned as constantly, and that smoke did not obscure the target or reveal the location of the shooter as easily.

Smokeless powder was seen pretty early as a very useful thing: even in the 1850's, nitrocellulose was thought to have a lot of promise. But the higher pressures had an unfortunate tendency to blow up guns- muzzle loaders especially- and the first military use came with the 8 mm Lebel rifle of 1884. A French general, Ernest Boulanger, was instrumental in getting it into service. He was one of the revanchists, the French thirsting for revenge against the Germans after their loss in the Franco-Prussian War. The adoption of a smokeless powder rifle set off a general scramble and Germany quickly followed with its own 8mm , the British with their .303 . So, something in the .300-.318 caliber range was established pretty early. There was actually a fair bit of variation in the calibers different countries chose, as they all fell into line. Lighter bullets meant ammo could be carried in larger quantity, but lighter bullets had shorter range and somewhat less effect. Heavy bullets above .32 would make an appearance in heavy game rifles, for the hunters, but as even .30 cal. could carry out to 1,000 yards and be quite effective, much above that for small arms just wasn't necessary. (The old 45-70 cartridge today can be loaded with modern smokeless powder and fired in modern rifles that can handle the pressure but , though no doubt effective against charging elephants, it's punishing to the shooter) . The Swedes went to 6.5 mm, as did the Italians and, initially, Japanese. ( The US Navy, seeing the importance of having light ammunition above all else, went for the high-velocity 6mm Lee, and a rapid-fire rifle to shoot it...but this bright idea was not much noticed). At the other end, the Germans kept 8mm for their Mausers, as did the Austrians, the Turks.... So, although you could say that there were a cluster of calibers around .30, there were a lot of different compromises: where to draw that line between portability and effect.. Eventually, of course, most militaries decided that small arms fire was largely close range, and began using rifles that fired lighter ammo very rapidly. Which is why the US army no longer carries M14's.