There is a lot of research and theory around fusion reactions with plasma, but is there a reason why plasmas cannot be used for researching other nuclear reactions, either in the lab or from astronomical data? I would assume that it might be because the plasma shields photons or charged particles from escaping?
It's easiest to make plasmas with light elements, so the only fusion reactions that are achievable are the hydrogen / helium / lithium ones, which are already pretty well understood. On top of this, a plasma is a chaotic environment with a lot going on. At best you will learn statistical and thermodynamic properties of the underlying interactions. Other types of experiments with a lot less going on and where the individual nuclear interaction partners and products can be tracked (e.g. lead-proton collisions at various colliders) are more interesting right now.