I think masturbation is appropriate and healthy in moderation, but it can also easily become a trap that leads to unhealthy behavior if left unchecked. So while moderate and excessive/compulsive masturbation must be judged differently, you cannot really judge one without considering the other.
As far as gender norms and modesty are concerned, I am a firm believer in equal rights and opportunities for all sexes and gender identities, so for me to accept any argument that one of them deserves a significantly different treatment than the other, I expect good reasons, not just a "that's how it is". If you were to argue that female modesty is more important than male modesty because that is a tradition you identify with, I can accept that as a good argument for living that lifestyle yourself, but not one an argument that is any good for convincing others outside that cultural circle of the same lifestyle.
Particularly in growing people, masturbation appears to me to be a healthy outlet for exploring your own sexuality and relieving sexual needs without engaging in dangerous behavior that risks anything from disease to unplanned pregnancy to exploitation by predators. And sexual exploration matters because young people need to learn to control their sexual expression and not to rely on outside enforcement for that control.
If there is one situation in which I would call moderate amounts of masturbation morally dubious, it would be in the context of a committed relationship. Not saying that masturbation while you have a partner is automatically bad, but you and your partner ought to be on the same page regarding whether using masturbation as a sexual outlet instead of waiting for an opportunity to do it with your partner is acceptable, or in what situations it is and when it is not.
As far as distractions are concerned, personally I spent way more time on sexual thoughts when I am denying myself orgasms than when I have them regularly. But I recognize that probably varies by individual and may have some gender bias in its variance as well. So your mileage may vary.
Finally, speaking of individual variance, I believe there is no one right system for everyone. How much masturbation is appropriate is something each individual must find out (or decide) for themself.