Automation and semi-automation through computational tools like LLMs are also making their way to deployment in research synthesis and secondary research, such as systematic reviews. In some steps of research synthesis, this has the opportunity to provide substantial benefits by saving time that previously was spent on repetitive tasks. The screening stages in particular may benefit from carefully vetted computational support. However, this position paper argues for additional caution when bringing in such tools to the analysis and synthesis phases, where human judgement and expertise should be paramount throughout the process.