The issue isn’t that Twitter doesn’t care. It’s instead a fundamental design flaw in the platform. Because tweets don’t exist outside of Twitter, when you’re banned, you’re done. For this reason, and because their business depends on a large user base, Twitter is hesitant to throw anyone off their service. They’re unwilling to tend the garden for fear of pulling too many weeds.
I think the Indie Web is the solution to many of the problems brought on by these social media silos. We just need more tools like micro.blog that utilize common protocols (RSS/JSON) to act as the plumbing that connects users together.