It's painful because it represents the relinquishing of hope. Hope that things are ever going to change, hope that the other person will ever stop treating you so poorly, hope that you can have the relationship with them you wanted to have, rather than the one you actually have. I actually think there is no more painful or illusory emotion than hope, particularly as it's so rarely we ever recognize it as the false hope it is.
There seems to be a disconnect in the understanding between many people who end up estranged. Those whose relatives instigated the NC often claim to have no idea what they've done, that it's happened for no reason; whereas the person who's walked away insists they are aware precisely why. I don't know the reason for this: some instances might represent the straw that broke the camel's back: they've tolerated the behaviour for year after year, then one day something - maybe even a small thing - proves to be the decisive moment.
If NC is done with the intention of achieving some self-serving end, or with the intention of punishing someone, it's horribly manipulative behaviour. But the schism is often as painful for those doing the cutting off as it is for those on the receiving end. If done as a self-preservation mechanism, it's usually a last resort. People procrastinate over letting go of the hope that things will ever be different because it represents a form of bereavement, even if you're grieving for something you never really had in the first place. And grief is painful. But acceptance does bring with it a form of freedom, enabling the process of letting go to begin, rather than living your life in the limbo of false hope. That's the reason it can bring about its own form of peace.
So not exactly 'bliss', but peace of mind is the endgame here, which might be seen as even more important. Sending empathy to all who have been through or are going through this.