This website suggests SDMH is incompatible with oxidizing agents, water. So it can be used for hypergolic purpose.This quote is from Sittig's Handbook of Toxic and Hazardous Chemicals and Carcinogens:
Properties of SDMH
Forms explosive mixture with air. A
strong reducing agent and strong base. Violent reaction
with strong oxidizers, strong acids, metallic oxides. Attacks
some plastics, rubber, and coatings. May accumulate static
electrical charges, and may cause ignition of its vapors.
And UDMH is also miscible with water and reacts with oxidizing agent. UDMH is often used in hypergolic rocket fuels as a bipropellant in combination with the oxidizer nitrogen tetroxide and less frequently with IRFNA (inhibited red fuming nitric acid) or liquid oxygen. The real difference between them is their melting point. The freezing point of SDMH is -8.9°C and UDMH is -57.7°C .UDMH has the lowest freezing point and has enough thermal stability to be used in large regeneratively cooled engines. Lower melting point ensures storing at low temperature for longer time & greater safety of this toxic chemical.So, this may be the prime reason.