Many parents have made the choice to be a great parent to their child, but do it from a separate household that their child's other parent. There can be many reasons a cohabitating relationship with a child's other parent doesn't work out, but that doesn't and won't stop parents from having a great relationship with their kids. If co-parents have a child custody arrangement (and most of them do!) they have to reference and abide by that agreement before making any big decisions. Big decisions, like moving your child out of a certain area, usually have to be approved by the child custody agreement.
This is to ensure that the move is, first and foremost, in the best interests of the child but for other reasons too. If a child were to move a significant distance from their other parent, how would that affect the custody agreement? It could impact how easily or how often the other parent could interact with the child and could impact the quality of their relationship. It could also change the cost of living for that child, say if a parent wants to move from the midwest to California, the cost of living would be different and could affect child support numbers.
In short, there is a lot to think about if thinking about moving a child a significant distance from their current child custody arrangement. It impacts multiple parties and since they each have their own specific viewpoint their could be disagreements about how to proceed. It is possible to tweak, or modify, the child custody arrangement to reflect a change of this magnitude. It just depends what a family would like to do and how they want to proceed.
Since child custody arrangements are tailored to individuals and their specific circumstances, a move can be fit in. However, parties have to be prepared to discuss, and possibly debate, the potential outcomes and changes. There are so many ways that a move can be a positive change for a child. This is why these requests are often approved.