It's probably down to snooty councillors. 'Street' has long had 'working class' connotations. (Look at the map of any major industrial city in the UK. The eastern side, where the workers lived among the smoke and dirt, is always full of 'streets'. The western side, where the bosses lived away from the smoke, has 'roads', 'avenues' and 'crescents). Wythenshawe was, at the time many of roads were named, a 'middle class' area, so there are no 'streets'.
Wythenshawe was fantastic when newly built - I used to really envy my cousins who had big clean new houses, gardens back and front, grass verges on their 'avenues' - it's sad to see how things have changed. It really was a sort of garden city idealised design for living.