The biggest problem is that you are removing the state from the class struggle. The state operates in the interests of the ruling class of a given society, be it capitalists or workers. Tax-funded programs in socialism aren't not socialist because a worker government is still socialist. It isn't about "true socialism," it's about understanding how the class struggle actually operates.

A useful comparison is the inverse of welfare under capitalism, which is private ownership under socialism. China is a good example, which has private ownership for non-critical secondary industries. It uses this marketization to help build up the productive forces to a level where planned economy can more effectively take over. This isn't a "capitalist sector" in the truest sense, it exists explicitly to build up higher forms of socialism.

You cannot cut a part of a whole system out and individually judge it in a vacuum. The necessary context that it exists in must be understood.