This would be an excellent quality of life change for PvP.
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Honestly I'd almost always have it, usually I try to keep a round or two on hand just in case, then when I have around 5 after some primary kills I will use the weapon more. Its actually got me to use a special more later in the game, ironically. If anything there should be a cap on how much you can earn/hold. I would echo what others have said though, always assume the other players have a round or two, and be more conservative with your special ammunition.