I think the thing is, there are vanishingly few families that have chosen to have an income low enough to qualify. Lack of qualifications, disability, caring responsibilities, single parenthood, housing issues, unemployment, whatever the reason for low income, there usually is a reason.
Whatever that reason is, it usually also has an impact on the children. Time spent at nursery goes some way to mitigating the impact of whatever circumstances mean the child qualifies.
I doubt the nursery workers treat the children any differently, and they won't go through life labelled, the whole point of this is that the gap gets closed so that they aren't any different by the time they get to school.
I know with Pupil Premium in secondary it's just something we're aware of. I don't expect any less from them academically, but we're aware they might need a bit of extra support because they may not have it at home, so if they don't have a pen, or they haven't done their homework because their electricity was off, or their parent is ill, or they left their book at their other house, they get a bit of extra support to rectify the situation for next time, or it's passed to pastoral who can find a way to offer support to the family.
I see plenty of PP kids whose families are fine, they don't have any of these issues, they just have a low income, so that extra support isn't needed, but it's better to be aware and not have to take action that not be aware and not be able to support if it is needed.
I really feel for kids whose parents work long hours to make just enough to pull them out of any additional help, but in doing so are less able to be present and supportive parents. I feel like those families slip through the cracks a bit.