
Slow practice matters, but its purpose is not to repeat one fixed slow tempo until it feels familiar. In adult practice, I find it more useful to treat tempo as a testing condition. At a very slow speed, notes, rhythm, hand position and tension are easier to inspect. At a slightly faster speed, problems that were hidden begin to appear. Returning to a slower tempo can then reveal details that were previously missed.
Motor-learning research shows that changes in practice tempo affect movement and timing, but the evidence does not support a simple rule that more variability is always better. Piano-based experiments have found different effects of tempo schedules on motor learning and transfer, and the most useful strategy may differ between novices and more experienced players.
A practical approach is therefore to move between several controllable tempo levels rather than chase speed mechanically. At each tempo, check again whether sound, rhythm and movement still hold together. What ultimately needs to become stable is not one chain of finger movements at one speed, but a musical structure that remains audible and controllable as tempo changes.
Sources:
https://pmc.ncbi.nlm.nih.gov/articles/PMC5832267/
https://pmc.ncbi.nlm.nih.gov/articles/PMC4128393/
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