Well, you can, but that would be fraudulent. But whoever you sent the DMCA takedown notice to, it's not their concern and not their duty to check whether you're the rightful copyright holder or not.
And then it would then be incumbent on the users to fight that?
They're not hurt at all by popcorntime going down.
That said, yes the DMCA can be abused. The check against that is the same check that exists against other kinds of fraud: it's illegal.