Why should any unit be used instead of the watt (W) as a power unit?
Simply because a watt is a measure of work done.  The real part of V*A is watts.  There are exact equivalents in mechanical systems.  \$W=\dfrac{J}{s}=\dfrac{N*m}{s}\$ so \${N*m}\$ here is Force that does work through a distance but it can also be a measure of Torque over a distance and that is static(non moving).  One is the potential to do work, one is the work itself.

Using watts for reactive power would be wrong because reactive power is stored power and not capable of doing work.

Using VAr - r for reactive is just short hand for the purely imaginary part, instead of using i or j (for you physicists out there).