The incentives are structured to make immediate takedown the path of least resistance. Yes, in theory, they can do otherwise; why would they spend money and effort doing otherwise?
Providers not liable under DMCA still do this anyway. It's not worth fighting for anything at all, to them. They'd rather lose your $10/month of revenue than take a 0.01% chance of a $100,000 lawsuit. Try getting a false abuse report on almost any VPS provider.
