IIRC, the .222 (direct parent of the .223) is the very reason for the existence of small rifle magnum primers in the first place, since they ended up piercing the thinner/softer regular small rifle primers a ton back when the cartridge was first being developed.
Correct. Although with lower pressures than the later 223 and 222 Rem Mag, a harder-cup primer seems barely necessary. So Remington developed the 7 1/2 for the new cartridge sometime around 1950. Although designated a 'magnum', the original version had the same explosive pellet as the standard # 6 1/2. (Other manufacturers have done this too in some cases as @markm87 says in post #5.)
When Remington later developed its .17 Rem cartridge, the 7 1/2 was uprated to be chemically 'hotter' too to provide satisfactory ignition in all conditions.
I did an SRP test in SR 308 Win Lapua 308 'Palma' brass some years ago, and found no correlation between MV levels and primer type as opposed to make/model. As MVs are related to chamber pressures presumably the latter too. This was unlike the results from a previous 308 Win based test series using LR brass and primers.
https://www.targetshooter.co.uk/?p=2662