The accumulation of votes is never linear, when we instantly remove a question from the active list for reaching a -4 score we create a system whereby only a couple users can collaborate to push a user's question off the home page. This abuse requires moderator intervention however users lack the tools to really "prove" they are being ganged up on. In other words, no one will ever truly know if this behavior is happening. As such, the "no cop, no stop" rule says we are actively encouraging this gang mentality.
I am aware of the experiment to not display negative votes. But that doesn't prevent the opportunity for users to abuse the -4 score home-page deactivation scheme.
My Proposal is simply allow new questions to simmer a bit, get some eyes on them, and after a grace period pull them off the active list.
I assume there is no jarring and injurious consequence to allowing a -5 score to sit on the board for a day or so. If the post is really inappropriate we have a flag system. Voting is a low-urgency privilege that gives best results under many eyes.
Consider the corollary: positive votes may have to wait up to 3 hours before the Twitter Bot announces them, yet the instantaneous treatment of negative scores invites abuse. I realize this discrepancy is a logistics issue, but it exists nonetheless.