I've had no problems with availability. None. But I know going into an award booking that I need to be flexible, both with my travel dates, my preferred airlines, and perhaps even my preferred airports. But I haven't had to sacrifice much, maybe +/- 1 day here and there, but that's about it. But I always, always book via the elite line unless it's a simple MSP-XXX roundtrip that is really easy to get on nwa.com.
That's the primary benefit of being Platinum, I guess. There might be better award inventory and the cost to do it all over the phone (or in-person at MSP) is exactly the same as at nwa.com, so I get to ask them to check the exact details I'm interested in.