I will start where undergraduate philosophising leaves us-- we fast because it brings us Joy. Not because it gives pleasure-- surely there is more pleasure in eating. And not because it makes us Happy-- in the sense that happiness is, in my mind, associated with a smile.
Now Joy, it is different. Notice how the Christian faith talks of Joy in Christ-- not Pleasure, and not Happiness. The reason is, that Joy can be experienced through pain (the permanent Joy of parenting is very different from the impermanent pleasure of it), and Joy can reside in a sad heart (I was joyed at giving blood to a severely injured friend but was, at the same time, sad. At his condition.)
The wise seek the telos to everything. The teleological explanation for Fasting, then, is Joy.
What is the teleological explanation for Joy?
I side with Schopenhauer-- Joy is produced by activities and experiences that increase our chances of survival as a species. As a species, not just as an individual. Whence the Joy in parenting and in blood donation. And in religion. And in Fasting.
So by what mode does Fasting increase the chances of survival? The obvious, corporeal answers, and not entirely a specious one, is based on control. It is so trivial that I will not belabor it.
A more abstruse ratiocination links Fasting to a Spiritual Final Cause, or purpose, or telos. This purpose is also shared by Religion, Meditation, Yoga, and Worship. I will leave that analysis to later.
However, to conclude: In my subjective analysis, as mentioned above, there is a direct link between Fasting and Joy. Clearly, fasting has intrinsic value.