A universe without stars would lack the chemical building blocks needed for a living entity to extract energy from the environment and thereby resist the pull of entropy.
The main difficulty with this suggestion is that all life requires a means for overcoming the second law of thermodynamics. Life requires the extraction of energy from the environment. Any life-form imaginable must therefore have systems that allow for something like metabolism and respiration, which in turn require a minimal amount of complexity (e.g., there can be no single-molecule life forms). Many examples of fine-tuning do not allow for such complexity, however. If there were no stars, for example, then there would be no stable sources of energy and no mechanism for producing the heavier...