It has a mid range tragejectory at 300yds of about 25% of .303 and about 50% of both .30-06 and 7.92

Only because it uses a puny 150 grain projectile, or is it a 148 grain. The 303 generally uses a 180 grain, while the 30-06 often has a 200 grain projectile.

The 7.62 NATO or 7.62 x 51mm (if you use metric then 7.62 x 51mm is what you’d describe it as… 7.62mm bullet calibre and 51mm length case.) was a post WWII creation that was basically designed to solve the problem at the end of the war… namely that the US used the 30-06, the Brits and the commonwealth largely used 303 ammo, while the French had their own 30 cal round and the Germans had the 7.92 x 55mm or something and the other european countries that were becoming part of NATO had other ammo types as well and of course Japan had their own 7.7mm round too… the first priority was for everyone to use the same rifle ammo. Everyone wanted their own cartridge, though the Brits wanted a new 7mm round they had developed for the Em-2 bullpup, but the Americans still wanted a round that could reach out to long range in a MG and rifle so the result was that the 7.62 x 51mm round was created… it really was a 30-06 with a centimetre cut of its case length.
The result was a round that was indifferent at long range but too powerful to be effective as an assault rifle round in full auto.

The 223 round was also a post war development… at the time they thought that velocity was a better killer than calibre or bullet weight because energy equations give a skewed more flattering result with an increase in velocity than they do with an increase in bullet mass. So a lighter high velocity cartridge has less recoil so it is easier for smaller people or less well trained people to use. It was intended as a sort of replacement for the M1 carbine in the AR-15 and was initially issued to US personel for guarding airfield duties. The results by the South Koreans in combat however showed it was effective and light if a little bit long in design. Lethality seemed way out of proportion to its calibre. (it was not actually the velocity but the fragmentation of the projectile that gave it its effectiveness.)

Of course various high power .22xx calibre rounds did exist before WWII and the number of 30 cal rifles before WWII was huge… most major powers in WWII were already equipped with 30 cal rifles, it was an established calibre, but the 7.62mm NATO round was developed for the purpose it was used for… to simplify the logistics of NATO forces.