Why are super absorbent polymers not made from polysaccharide-rich wheat straw and chaff?
Until the 1920's, polysaccharides were a prime choice for producing absorbent materials. However, their water absorbancy was limited to about 10:1 by mass (i.e. 1g of materiel could absorb 10g of water).  This metric, along with absorbancy by volume, are the properties of interest when designing a super absorbent polymer (SAP).  

Subsequently, for several decades hydrogels dominated the SAP landscape. According to this Wikipedia article:  


  "Water-absorbing polymers, which are classified as hydrogels when
  cross-linked, absorb aqueous solutions through hydrogen bonding
  with water molecules. A SAP's ability to absorb water is a factor of
  the ionic concentration of the aqueous solution. In deionized and
  distilled water, a SAP may absorb 300 times its weight (from 30 to 60
  times its own volume) and can become up to 99.9% liquid...
  [...]
  Superabsorbent polymers are now commonly made from the polymerization
  of acrylic acid blended with sodium hydroxide in the presence of an
  initiator to form a poly-acrylic acid sodium salt (sometimes referred
  to as sodium polyacrylate). This polymer is the most common type of
  SAP made in the world today.
  
  Other materials are also used to make a superabsorbent polymer, such
  as polyacrylamide copolymer, ethylene maleic anhydride copolymer,
  cross-linked carboxymethylcellulose, polyvinyl alcohol copolymers,
  cross-linked polyethylene oxide, and starch grafted copolymer of
  polyacrylonitrile to name a few.  


There is also ongoing research into improving the ability of natural products to perform as SAP's.  According to the same Wikipedia article quoted above:  


  "Today´s research has proved the ability of natural materials, e.g.
  Polysaccharides and Proteins, to perform super absorbent properties in
  pure Water and saline solution (0,9%wt.) within the same range as
  synthetic polyacrylates do in current applications."  


Summary, TL;DR:
Until the 1920's, polysaccharides were the prime choice for producing absorbent materials. Primarily due to their relatively low absorbancy (~10:1 by weight, and lost water when pressure was applied), they were subsequently replaced with hydrogels (absorbancies of 50:1 to 300:1, and maintained water when pressure was applied). However, by the 1960's, polysaccharide based super adsorbent polymers (SAPs) saw a resurgence in use as researchers (primarily at the US Department of Agriculture) were able to re-engineer polysacharide based SAPs to have absorbancies comparable to that of the synthetic hydrogels.  

The qualities that make a SAP desirable are primarily it's absorbancy and ability to maintain absorbancy under pressure, but also cost and availability of materials. It is the latter of these that drives the research to develop better techniques for the use of polysacharide based SAP's.