There are a bunch of misconceptions in your question:
1) General relativity is a field theory, first and foremost. While we can certainly talk about energies and such in this contect, it is not the most natural language for the theory, which is phrased in terms of the fields themselves--where is the potential energy in an electromagnetic field distribution? Where is the kinetic energy? They're tied together a lot. The natural thing in these theories is the fields and their field equations. In this context, dark energy, expressed as a cosmological constant, is one of the simplest possible formulations
2) In general relativity in particular, the notion of global conservation of energy is a very tricky one. This is because there is no natural time coordinate to use to find the congugate energy. There is a special subclass of solutions, those of asymptotically flat spacetime, where there IS a notion of global conservation of energy. Simple examples of these solutions would be those describing isolated black holes. Unfortunately, most cosmological models are NOT asymptotically flat. So talking about the conservation of the TOTAL energy of the spacetime is meaningless.
3)Dark energy, in a simple energy analogy, would probably be better thought of as adding more negative potential energy--it certainly is the case that, as the universe expands, we're getting more dark energy, not less. So, thinking of this in terms of dark energy getting converted to KE is an incorrect way of viewing the model.
4)People believe the model because it is the simplest model that fits the data. There are simple extensions that add complexity that would satisify some of your concerns. It is also still possible, though increasingly less probable, that we live in the universe described by one of the void models.