Did Erin Hunter have to go and kill Silverstream?

For her story plot to go as she planned, yes.

Erin Hunter had to kill Silverstream so that she and Graystripe's kits would be with RiverClan when Tigerstar became the joint leader of RiverClan with Leopardstar. Then Tigerstar, in his quest for pure-blood cats, could try to make Stonefur kill them and if Silverstream were still alive, she would protect her kits and she wouldn't let Tigerstar try to kill them.

If Tigerstar wouldn't have tried to kill the kits, then Graystripe, Ravenpaw, and Firestar wouldn't have rescued the kits, and the plot of the story would fall apart.

So, yes. Erin Hunter did have to kill Silverstream.