Consider SMTP, which is a true peer-to-peer system. In SMTP, abuse is a solved problem - spam filters work great, and 33mail/mailcatch (disposable email) improves things tremendously. At most 1-2 recruiters/SAAS offering marketing automation/etc slip through my filters each week, forcing me to expend about 3-5 seconds/week clicking "report spam".
The "abuse" problem on twitter is similarly not really a filtering issue; if it were, then it could be easily solved by a moderately better twitter client or switching off notifications of @mentions.
No, the actual problem people face is that they want to stop others from speaking, and label the speech they wish to stop "abuse". What's scary to most (including me) about Twitter is that an angry mob may form and decide they hate me, and then use Twitter to coordinate real life actions against me.
That's not a problem of abuse on the platform; that's a problem that the platform enables people to speak among themselves in ways I dislike. Lets be clear that this is the problem some folks wish to solve. It's only by identifying the problem that we can properly solve it, or decide if it's a problem that should be solved.