You had the Spanish American War ending in mid 1898. This is the watershed that caused all this. The Battle of San Juan Hill convinced everyone that the 30-40 Krag wasn't cutting it. They tried in 1899 to bump up the Krag's performance, but the Krag couldn't cut it. This started the search for what became the 30-03.
The Mauser was the stronger action. They could copy it, but they couldn't quite copy the powder. They also had in mind a different performance envelope. The wonks wanted something that would shoot the same 220 grain bullet as the Krag, only farther. DuPont delivered a powder that could do that, and thus the 30-03 was born.
Almost from the start, they saw the problem. Launching a 220 grain round-nosed bullet cause all kind of problems. It caused barrel erosion. It caused a big looping trajectory. The 30-06, with a smaller pointer bullet fixed all that, but they kept using the same DuPont powder.
WWI happened. By war's end, everyone had seen what the 30-06 could do, as well as all the other chamberings. 30-06, .303 Brit and the 8mm Mauser. The powder chemists had also been working on the problem. 300 Savage is a civillian attempt to adapt and improve.
1) It was supposed to be an improvement on the 303 Savage's performance in the same way 30-03 improved on the 30-40 Krag using existing components where possible.
2) It used the new powders developed after 1900.
3) It produced 3600 fps with a pointy 150 grain bullet which put it into the same ballpark as military rounds like the 30-06 (close, but not quite).
4) It could do all this in an existing lever action package that did not require a lot of redesign.
France and Britain both looked at this development. I don't have access to what the Brits did, but the French developed the 7.5X54 for their new MAS 36 about 7 years after the 300 Savage. The Americans started to play with the idea, but it didn't produce a cartridge until after WWII-- the 7.62X51. Nobody took the 300 Savage and stole the idea, but a lot of people were working on the same problem and Savage just had a product out there earlier than the others.
. . . at least that's how I understand it.
Only things I would argue in that is that #3 should be 2700fps rather than 3600fps (I know it was a typo), and that the 300 Savage used new powders designed probably after 1915.
Add that the 300 Savage was another Savage cartridge almost surely conceived and prototyped by Charles Newton, and finished by Savage engineer Charles Nelson (like the 250-3000 was). Charles Newton was definitely a guy who kept up with powder developments.
