Jeff Davis had left Richmond and came west to Murfreesboro in November 1862 to meet with Bragg and with Johnston in Mississippi about keeping the Mississippi valley, especially Vicksburg, open and countering Grant's advances. One of the problems with having Holmes repeating Van Dorns abandonment of Arkansas and moving his army east of the Mississippi to re-enforce Pemberton was that it meant giving up control of the west bank of the Mississippi River to the Union Army and Vicksburg would become meanless anyway.
This was all a part of the Confederate defensive efforts in Arkansas to keep as much of the Union Army as possible tied up protecting Helena, as a fueling depot for the federal steamboats. While on the other hand harrassing those steamboats as they traveled the river. The threat of the CSS Ponchartrain also played a part in this as the Federals didn't true know her status, whether she was seaworthy or not.
Not much real thought was put into defending Little Rock, outside a generalized plan, until July and August of 1863. And while the fortifications in front of Little Rock were pretty good, no simular sized army in the world could have protected all the fords north and south of Little Rock during the drought conditions in the summer of 1863. And to have abandoned Little Rock would have meant abandoning such things as the CSS Ponchartrain. And while fortifing Pulaski Height might have been a stronger position what good is fighting for fighting sake, if you have already lost your main objective?
The fault I see in the Battle of Little Rock is that Price failed to plan for and orderly withdrawal once his flanks were turned. He had to have know that he would be eventually Flanked.