Standard Japanese story age. Because an adult is too old to be the lead in RPGs, for example.
There's different standards, but 14 is the norm for magical girls and mecha pilots (remember those?) whether they actually be 14 or 28 like in Eva or what have you. I wouldn't dwell on it too much beyond framing and genre convention.
There's a fairly decent amount of 21 year old RPG leads though they tend to be grizzled military veterans at that age. Cloud Strife, Lightning, Yuri Lowell, Alphen, etc. If you're looking for grizzled veteran magical girls I guess there's Spec Ops Asuka.