If Sure Start centres were attended by 'good' parents, as well as parents in need of support, that can only have been a benefit and a good thing.
Firstly, no-one else can judge just how much a parent (usually a mother) might need help - she can be wealthy, well-spoken, educated, and still struggle massively with some or all aspects of parenting a young child.
Secondly and more importantly, a universal service is more acceptable to many people, whereas targeted services are stigmatising. We see the same principle with pensioners who will take the state pension that they have 'earned' but will not touch any means-tested benefits.
Struggling parents, of any social class, are more likely to attend a place that 'everyone' goes to. The poor, uneducated mother won't feel singled-out if every other mother she knows or has seen locally is going to the centre too.
Also, a place that 'every' parent goes to encourages mixing of people from different backgrounds, helping integration and cohesion and community.
Those who then don't attend, can be flagged for follow-up - are they unaware? or are they feckless, lazy, disaffected, anti-society, and their children in need of a great deal of support?
It is a mistake that both left and right make, to think of means-testing or targeting as a way of saving money, when in fact that undermines the whole service, sometimes to the point of it becoming entirely ineffective.