Why didn't Saruman go to the Shire to take the Ring?

[Gordis]

Originally Posted by William Cloud Hicklin

No, not diverted from DG to Mordor; rather, the army from Udun and the Morannon, originally slated to march north and join with that of DG, was rerouted westward into northern Gondor. This was motivated (I speculate) by S's conviction that the Ring was in Gondor; but also by the military necessity of dealing with the Rohirrim, whom Saruman was supposed to have neutralized.

Makes a lot of sense.
As for dealing with the Rohirrim: a see a slight problem.
I somehow don't see Orc infantry as being effective against trained cavalry. I doubt the Orcs could maintain rigid formation which is criucial for repulsing cavalry. So, this army from Morannon sent against the Rohirrim most likely was composed of Haradrim and Easterliing cavalry. (In fact, that's what Theoden had dealt with). But if it were the same contingent that was supposed to march against Lorien, of what use would the cavalry be in the Wood?

I don't know if this bit is in the excerpts from the Chronology ("Scheme") published in the RC, but it's in the complete document.

You were able to read the unpublished Chronology? Cool!

(One can just imagine the cursing and blows in Mordor's quartermaster corps that resulted when Lugburz moved up the whole timetable to 10 March!)

If Lugburz also changed the direction of the main blow from Lorien to Minas Tirith, that would lead to some cursing indeed.

[William Cloud Hicklin]

As for dealing with the Rohirrim: a see a slight problem.
I somehow don't see Orc infantry as being effective against trained cavalry. I doubt the Orcs could maintain rigid formation which is criucial for repulsing cavalry.

Actually, they did exactly the right thing- this was the army which blocked the Road to cut the City off from reinforcement/relief, and which according to Theoden's scouts had dug trenches across it and planted sharpened stakes- which the Rohirrim themselves acknowledged would break a cavalry charge. Fortunately for the good guys, they didn't know about the Stonewain Valley.