Run the gamut did not originally mean running wildly from one thing to another. It began as a musical expression. In older music teaching, the gamut was the full range of notes in a scale. To run the gamut meant to move through that whole sequence.
Over time, the phrase widened in meaning. Today it usually means to cover an entire range of something, especially a wide variety of feelings, qualities, or possibilities.
- The reviews ran the gamut from praise to harsh criticism.
- Her emotions ran the gamut from fear to relief.
- Prices run the gamut from cheap basics to luxury items.
A useful contrast: people sometimes assume the phrase is about speed or chaos because of the word run. But the key idea is not rushing. The key idea is moving across the full span of something. That is why the phrase works so well for ranges of opinion, cost, mood, or style.