Why is amyloplast produced by some plant cells but not other cells?
Amyloplasts are non pigmented organelles responsible for plant sugar storage, release and gravity perception (or tropism). This being the case they are commonly found in root caps (for gravity) and storage sites like tubers, fruits and grains. 

So due to cell differentiation, it is not possible for these plastid organelles to be present in all cells the same way chloroplasts (another type of plastid) is not present in the stem (with the exception of small plants and succulents) and most of the root cells (Reece Urry et al, 2011). 

Reference

Reece J.B., Urry L.A., Cain M.L., Wasserman S.A. et al (2011). “Campbell Biology 9th ed” Pearson Education, Inc., publishing as Pearson Benjamin Cummings, 1301 Sansome St., San Francisco, CA 94111.