[Brent Hutto]

I think it depends in part of your skill/experience level vs. the demands of the thing you're learning.

For many players with only a few years (or less) of experience, they don't really have that automatic mode that lets them play groups of notes quickly and automatically as one unit. So for that level of player, starting slowly and gradually sneaking up on a tempo fast enough for performance is the only way that's going to lead to a good result.

But once you develop the more advanced skills where your thinking and your fingering is operating very efficiently on entire chunks of notes, you probably need to decide if a given tune or a given passage is going to be play in fast mode or in one note at a time mode and practice accordingly.