To understand why learning about black bodies is useful despite their absence in nature it is useful to answer your second question first. The reason a black body can't exist it nature is because it's boundary, the outer layer, would have to be non-reflective and perfectly transmitting. This implies a few things but most importantly that the boundary needs to be infinity thin for the transmission and not smooth. It can't be smooth because radiation hitting a smooth boundary always needs to reflect some part of it's energy when transitioning to the new material. For some extra info on this see the Fresnel Equation.
So why do we learn about perfect black bodies? Well because of two reasons.
- It is a model of reality that is easier to understand and does share some properties with reality. Or it's properties are related to the real properties via some parameter.
- Near perfect black bodies, systems that are close enough to being perfect black bodies, do exist and studying them as if they are black bodies can teach us things about the system that would be much harder to discover without this idealisation.
In physics as a whole, and many other STEM fields, it's often not useful to look at details that won't change the overall picture. In relativity it's common to ignore the rest mass of hyper relativistic particles because it won't really influence the total energy of the particle because the total energy is much bigger then the rest energy. In thermodynamics the ideal gas law is used to model gasses despite an ideal gas not existing. However hot gasses are close enough to an ideal gas that as long as the conditions are right the ideal gas law will give correct predictions.
In short, yes perfect black bodies don't exist. But that does not make them a useless model of reality.
As this question's answers explain, one thing that can be modelled as a black body is a black hole. Which helps us study this phenomenon.