I have used Magnum primers in all the calibers that you have listed, including .223. However, my best load in the Savage 110FP .223 that I used to own, was with a Rem 6.5 (non-mag) primer.
For instance; I see from my reloading journal, dated 4/7/02 (Sunday, AM, 60-65 deg, 0-10mph), I was shooting a Rem 700 Varmint Synthetic in .22-250 Rem and a Rem 700 Varmint Special in .243 Win. I used the Rem 9 1/2M primer with 36.0gn of Varget, virgin Rem brass and a 40gn NBT to shoot a .185" with the .22-250Rem and I used the 9 1/2M primer with 43.0gn of H414, virgin Rem brass and a 87gn V-Max to shoot a .453" with the .243Win.
I used the Rem 9 1/2M in the .25-06 with RL22 and the Barnes 100gn TSX. Scary accurate and deadly on whitetails. Required? no, I just stumbled upon an accurate load while doing load development and experimenting. JohnnyK.
Note: the above group for that .243Win wouldn't normally get honorable mention, but it was the best group the Hornady's ever shot in that rifle. For me, I have on several occasions found that Hornady bullets do not provide the gilt edge accuracy that I have readily obtained from Nosler Ballistic Tips and Sierra MatchKings.