My approach is remarkably straight forward. I listen. If something bothers me with how it presents sonically, I work to lessen it. If I find something is missing, I work to bring it forward. Measurements can be of great help to find the source of the problem.
Thank God for our ears. Not to mention that any comment about audio without comparative listening is nonsense. As for determining what room correction might be required (for tonal accuracy, content resolution, transient response, etc.), we can easily aid it by using good headphones with a good amp and doing comparative listening with the speakers in front of you. Not surprisingly, achieving a good tonal accuracy will also result in improving all other parameters. Remarkably, you will find that sometimes what you hear from speakers you may personally prefer on some tracks, while, clearly, headphones are a superior sound device (apart from the sound stage alone). Arguing those results among listeners might be a sufficient thread for this forum, but it would make no practical sense because it is related to individual psycho-acoustics (including emotion) and may even include some missing variables that can not be discussed because they are not even determined. In short, listening, adjusting/experimenting to A/B comparing, and ending up with YOUR acceptable compromises, is the only process worth trying; disputing or arguing it here is a complete waste of time. Reporting it, however, should be encouraged and appreciated, not ridiculed.