Because as it is now, if you have a clique that's in power, but another group manages to topple them, the new group will have some chance of putting their own people—which is to say, new people—into positions.
If, on the other hand, we instead let people appoint their own heirs, a) many of them would appoint their own family members (or, if we forbade that, would find someone to swap off with), b) the old clique in a situation like that above would be able to maintain their power even through a coup, as they could ensure that all the positions their people occupied remained within their group essentially forever, and c) in general, it would just be terrible for turnover, especially for positions which are presently elected, as even if you managed to wound, capture, or even kill the "old guard" guy holding the spot, rather than getting to replace him with someone new and fresh, you would be 100% guaranteed that his buddy, also part of the old guard, would be the one to get the position.