Monastic tradition features use Wisdom only to calculate saving throw DC-s.
The Way of Shadow practically does not use it at all, only as the DC against minor illusion.
The Way of the Open Hand uses it for
- All 3 options of the Open Hand Technique
- Save for sanctuary from Tranquility
- Save versus the effects of Quivering Palm
All play a major role in the subclass.
The Way of the Four Elements uses Wisdom as a save DC against all spells and effects that need one (and 12 out of 17 options do).
While none of the subclasses "wastes" a high Wisdom score, Open Hand and Four Elements depend on it rather heavily, while Shadow pretty much ignores it. Note however, the features from the Monk base class also use Wisdom.