My 'can't sing, won't sing' dancer did her first song and dance solo at a festival back in May, so never say you child can't sing AT ALL.
As far as tap is concerned, it depends a lot on how good she is at other genres.
A serious ballet dancer looking for a ballet career - so aiming for Ballet at one of the 'named' dance schools - would, in fact, be encouraged NOT to do tap. Something about incompatible technique / use of feet and ankles? For such a child, ballet (lots, including probably at associates class) and contemporary would probably be the most critical.
However, an 'all rounder' - someone looking to go to an all round dance college to train as a performer or a teacher - should probably do tap. Partly because in almost all 'children's dance schools', junior teachers would be expected to teach ballet, tap and MT / Jazz classes - it would limit employment opportunities if such a teacher could only offer 1 or 2 of the genres. Also because, if she might ever want to go into the business as a performer, offering the widest possible package would maximise the (slender) chances of employment - 'we're looking for a dancer who can do some jazz numbers, one with a some acro / gymnastic skills and then the big tap finale'.
DD's dance school sends several pupils to dance college every year, all of whom have studied ballet, tap and modern theatre (as in the dance style, not the singing part), are trained to sing at least in choirs and enough solo to pass an audition, and have done solos and larger group dances of all types including contemporary, lyrical, national, character, ballet, usually song and dance, tap and modern theatre dance. It has sent pupils to pure ballet schools, often rather younger, and those children didn't always do tap - so whether to drop tap is partly an 'is she good enough at ballet to follow a ballet-only route?' question.