Trolls aren't the primary problem with the [US] patent system. They're just the problem Congress is willing to fix. The primary problem with the patent system is, well, the patent system. The system makes it too easy to get broad, vague patents, and the litigation process is tilted too far toward plaintiffs. But because so many big companies make so much money off of this system, few in Congress are willing to consider broader reforms.
The problem of large companies exploiting the patent system hasn't gone away. If anything, it's gotten worse as the courts made it easier to get broad, vague patents in the 1990s and early 2000s.
A modern example is Microsoft, which has more than 40,000 patents and reportedly earns billions of dollars per year in patent licensing revenues from companies selling Android phones.