Let me correct a misconception you seem to be carrying. When an admin with long experience of one of our long-term abusers identifies a pattern of behaviour matching that abuser, you would be *amazed* how often CheckUser reveals that the IPs are either the same or open proxies.
So what? The point is, there's a systemic problem where people who AREN'T affiliated with with banned editors are routinely being falsely accused. It doesn't matter how often the "reminds me of a banned user" test is right-- the point is, sometimes it's wrong we need to stop callously throwing around charges that aren't justified. ****** Yes, Alec. It's good to stop callously throwing around charges that aren't justified.
Neither checkuser nor sockpupet investigation is 100% accurate. We do our best, but no human endeavor is going to be perfect. When people seek to resolve the mistakes in a reasonable way these things get cleared up pretty quickly.
What happens in practice is that blocked editors who make the most noise about "injustice" are almost always the ones whose blocks and bans were very well deserved. And even then it is quite simple to get reinstated, if they do us the courtesy of believing we're sincere: just wait by the sidelines until the block expires, or if it's a ban take a few months' breather and send a polite request for reinstatement, promising not to repeat the behavior that led to the ban.
What that requires is patience. Sometimes it also takes grudging acceptance of a consensus decision that went the other way or of a policy that's necessary for the project's overall health (but that causes a few inconveniences in one's own particular case). There are very few exceptions where an editor who acquires those traits couldn't come back.
-Durova