I think it's interesting that a debate about vocabulary can turn into a debate about phonics, though, because it is a phenomenon that I have noticed when teaching rather older, KS2 children (in general MC, in general with supportive, decently educated parents).
There seems to be a feeling amongst these parents that to 'support their children's academic progress' means to do some very specific, narrowly-focused things: to do workbooks, maths worksheets, online learning such as MyMaths or repetitive offline learning such as Kumon, to practise spelling in isolation. They often react in surprise when i suggest that to improve their child's writing they should read books together or discuss their child's currrent reading book with them, visit places of interest or watch TV documentaries together and discuss them.
Similarly, I wonder whether parents are 'doing phonics' with children - watching alphablocks or online games, working through phonics readers, pointing out words and letters - almost INSTEAD of reading books for enjoyment, singing nursery rhymes, talking and discussing around play and general experience of the world around them. Or 'doing number work' rather than playing dice games, hopscotch, number songs etc. So doing 'pre school school work' in a narrow sense rather than developing vocabulary naturally IYSWIM?