The prosecution certainly did rush this case to trial. The prosecutor should have known better than to indict Westerfield before he had all the evidence he needed for a conviction, assuming DW is even guilty in the first place. The defense did not request an early trial. DW simply refused to waive his right to a speedy trial. All the blame for a hurried prosecution case must be laid at the feet of the prosecutor, not the defense.
This point has been made before and explained. For your benefit, I will explain again.
Defense has right to a SPEEDY TRIAL. It is guaranteed. The reason they do is to keep LEO's and DA's from jumping the gun and arresting some suspect just to make themselves look good before they have enough evidence to prove their case. Looks like the DA and LEO's jumped the gun on this one, according to you.