I'm a huge proponent of triage incident response. So much so that I developed procedures based on the idea that gathering a little information from key data points early can lead to an accurate assessment of the situation without having to conduct laborious processes such as creating a full disk image all the time.
Triage saves time and effort. The purpose of triage is not to conduct a full analysis. The purpose is to 1) sort and prioritize and 2) gather enough information to decide whether or not to continue an investigation. It also maximizes the effectiveness of analyst, systems, and tools.