Why do plants not have fat cells, and store their reserves in vacuoles instead?
Short answer
Parallel evolution can generate similar traits in unrelated organisms based on unrelated structures.

Background
First off, the question is based on a few misconceptions: 


First, you are making an apple-and-pear comparison; Fat cells are cells - vacuoles are organelles. Fat cells store fats in liquid droplets, called adiposomes, which are lipid-rich cellular organelles that regulate the storage and hydrolysis of neutral lipids and are found largely in the adipose tissue. Vacuoles have a variety of functions, namely 1) contribute to the rigidity of the plant through hydrostatic pressure; 2) store nutrient and non-nutrient chemicals and 3) break down complex molecules. The latter two functions are quite reminiscent of the function of lipid droplets in animalia.
Plants do not store energy reserves in fats like animalia do. Instead, plants store starch, which is not a hydrophobic lipid, but a hydrophilic glucoside polymer.


Apart from these specifics, the question can be tackled more generally - unrelated organisms can solve the same 'problems' (like storage of energy rich compounds) through parallel evolution (wings in bats and birds for example). Why does a bat wing contain fingers and a bird's wing doesn't? Because they developed the ability of flight through different, parallel adaptations.