MITRE ATT&CK™ Matrix
MITRE has developed a framework to catalog TTPs. It's an excellent, systematic way to tackle known TTPs. The attack matrix can be a great source to implement test cases to ensure that detections are in place and working.
Having a systematic approach to ensure that known TTPs are detected is a great way to grow defense capabilities. However, the systematic approach of building and testing (and hopefully automating) these could—but probably should not—be performed by the offensive security team. The task is a rather generic engineering task that doesn't necessarily need the unique creative skill set of the offensive team.
The offensive team should help augment the attack matrix and discover new missing areas. Most important, however, is that someone in your organization becomes familiar with the ATT&CK Matrix to ensure a holistic understanding of the publicly known TTPs.
