Why didn't rishis cut their hair
We all know that Jatas or Long hair is mark of identity for rishis in Hinduism. Which is also called as "Jata Mukuta" Rishi's and muni's were doing Tapasya , Meditation etc. for long years ,during which these hair and beard used to grow longer.
The Rishi's on the other hand do not used to give much importance to body decoration or beautification.They were not supposed to care much about physical body,so they simply used to stop caring about the growing hair and beard . As caring and thinking about physical organs /parts and their well being is considered as material thing which is an obstacle in the path of Moksha i.e. Samadhi /meditation/yoga etc.
And I think they also used to tie hair like a crown for ease and for hygiene purposes.
Did long hair give them some power ?
Keshin Hymn, Rig-veda 10.136 tells us about long haired ascetics Or longhaired sage.
केश्यग्निं केशी विषं केशी बिभर्ति रोदसी |
केशीदं जयोतिरुच्यते ||
मुनयो वातरशनाः पिशङगा वसते मला |
वातस्यानुध्राजिं यन्ति यद देवासो अविक्षत ||
1 HE with the long loose locks supports Agni, and moisture, heaven, and earth: He is all sky to look upon: he with long hair is
called this light. (2) The Munis, girdled with the wind, wear garments
soiled of yellow hue.
They, following the wind's swift course go where the Gods have gone before.
This hymn also shows us the relation between Rishi /Muni /Yogi having jatas Mukuta and their spiritual powers. which means that the Rishi's (sage) muni's or the wearer is associated with spirits, and can travel in between worlds and their association with Agni.
We can read the Rig-Veda Keshin Hymn here.
From primary search in scriptures /puranas I haven't yet found any story or mentioning of direct relationship between Yogi /Rishi / Munis powers and their long hair but they used to earn the powers /siddhis etc. through long tapas/meditation only ,during which the hair & beard used to grow longer and they also used to tie those long hair in the form of crown.