You are on the right track with those three metrics, but you are missing one, and that is the “intext” operator. Also, those particular operators are only accurate for single-word keywords. You need to use the “all” prefix for multi-word keywords.
I suggest you ignore folks that tell you these metrics are unimportant, in reality, they are the most import metrics since SERP rankings are based on these primary signal groups. Search engines rank web pages based on relevancy scores. They combine the relevancy scores from those 4 primary signal groups to form a total relevancy score which is used to rank results on the SERP.
By looking at the the top results using these operators you are able to pinpoint where you and your competitors stand in regard to each of these primary signal groups. You can spot where you, or your competitor, are weaker or stronger. This allows you to focus on distinct areas of improvement and measure your progress, or lack thereof.