I have been able to get award tickets with some flexibility.
I have redeemed some miles at the saver level. I redeemed domestic award tickets (for 2 people) recently at the lower (saver) level. It took some flexibility to get good flight times, etc. I even did an award for myself for Christmas travel. (it would cost approx $450 to buy one ticket for this domestic destination).
I even redeemed 100K miles for a LH F award to Germany 1 1/2 years ago. Even changed the return date w/o problem. (note: the change is only allowed if travel has not commenced).
Some airlines are harder to get availability than others. I have redeemed saver miles for biz seats to Australia 330 days out.
With flexibility and good knowledge, one can redeem saver award tickets.