I have a question about this technique...

I've seen some teaching methods that say you should anchor the fingers of the left hand on the fret board until it's necessary to move to the next string. Like if you were playing a chromatic sequence (1, 2, 3, 4) you would keep the first three fingers pressed on the frets behind the fourth finger then move to the next string and start over again.

But other methods say you should lift each finger as the next one comes down to develop a more flowing hand as well as greater finger independence/strength.

I suppose it's a matter of opinion but I'd like to see what others have to say about their experiences with either approach, the pros and cons of both so to speak.

Thanks for any insight.