The membrane would be too rigid. The unsaturated fatty acids allow the membrane components to maintain their fluid mosaic structure-the components slip past each other freely and adjust to changes in osmotic pressure within the cell.

Further Explanation:

Lipids consist of fatty acids forming the hydrophobic tail and glycerol forming the hydrophilic head; glycerol is a 3-carbon alcohol that is water-soluble, while the fatty acid tail is a long chain hydrocarbon (carbon-backed hydrogen) of up to 36 carbohydrates.

Their polarity or arrangement can confer hydrophilic and hydrophobic properties on these non-polar macromolecules. Small water molecules can pass through the phospholipid bilayer through diffusion into the extracellular fluid or cytoplasm as a semi-permeable membrane, both of which are hydrophilic and contain large concentrations of polar water molecules or other water soluble compounds. The heads of the bilayer are hydrophilic the bilayer are attracted to water while their water-repellent hydrophobic tails face towards each other- allowing molecules of water to diffuse across the membrane along the concentration gradient.

Other components include:

Cholesterol: The comparatively rigid cholesterol anchors other molecules attached to the membrane, maintains membrane stability or structural integrity, and helps to separate some lipids, helping with membrane fluidity at low ambient temperatures.
Transmembrane proteins are embedded from the extracellular fluid into the cytoplasm within the membrane, and are sometimes attached to glycoproteins (proteins attached to carbohydrates) that function as cell surface marker.