If it were possible to separate public services into a public good aspect and a private good aspect, then government could probably ensure better outcomes for the poor by focusing primarily on the public good aspect.
A public good is both non-rival (the consumption of a unit does not reduce the units available for others) and non-excludable (it is not possible to include some while excluding others from this good). For example an illiteracy free community is a pure public good that demonstrates both non excludable and non rival qualities. It is non-excludable as it is not possible to exclude someone from the benefits of an illiteracy free jurisdiction while including others; and non-rival as one person consuming an illiteracy free jurisdiction does not reduce the stores for others. The private good have both rival and excludable characteristics (the consumption of a unit reduces the availability for others and it is possible to include some while excluding others during consumption). Alternatively a school is a private good - it is rival (there are only a certain number of children you can fit in a classroom) and excludable (you can be excluded if you do not meet certain socio-economic standards).
Assuming that all public services have rival and non-rival, excludable and non-excludable characteristics, it should be conceptually possible to separate the public good aspect and the private good aspect.
The Community Led Total Sanitation (CLTS)  movement has demonstrated that this distinction between public goods and private goods is not only possible but that it also delivers better outcomes for the poor. The CLTS approach encourages government, NGOs and collectives to focus on the eradication of open defecation (non-rival and non-excludable) whilst promoting greater freedom of individuals and markets to innovate in the provision of rival and excludable sanitary hardware. In less than 5 years, more than 90 million people in Bangladesh have gained access to (and are using) latrines as a result of this shift of government and NGOs away from the promotion of latrines towards the creation of a desire to eradicate open defecation.
CARE Bangladesh has also demonstrated that this distinction can be applied to the safeguarding of food sufficiency. In local communities in Rangpur District, the realization that extreme hunger in the ‘monga ’ period not only results in agonizing deprivation but also adversely affects landlords (who can’t access labour after the ‘monga ’) has led to a collective desire to eradicate extreme hunger. In some communities, all local households decided to invest one handful of rice per week into a common pool to be accessed by those suffering from extreme hunger. In other villages, public areas have been used for the cultivation of indigenous potatoes for the poor. This collective desire to eradicate extreme hunger appears to inspire innovative local approaches to safeguarding the food sufficiency needs of the poor.
This distinction is theoretically possible in sectors such as education and others. In such scenarios, the core role of government would be to focus on safeguarding the public good aspect whilst allowing individuals and markets to allocate the private good aspect in the most efficient manner possible.
Focusing on the provision of pure public goods resists elite capture and creates better incentives for the wealthy to include the poor. Such non-excludable targets are also relatively easy to monitor because ‘a single exception proves the rule’. As demonstrated in the sanitation sector in India, central and state governments can potentially leverage this through the provision of performance based funding to local governments (i.e. Nirmal Gram Puraskar  , Sant Gadge Baba program ).