Bruce Schneier and Gregory Maxwell have both stated that they believe the constants chosen for NIST's P curves (i.e. P-256r) are cooked. DJB has put together a detailed list of red flags but, outside of the suspicious constant, everything else appears to be potential implementation issues.
What kind of a speedup could they gain from cooking the constant?
Note: I'm aware of related questions, I'm looking for more of a high-level takeaway.