... but grammatically there should have been that word 兼.
Spin Lee's answer already pointed out that 兼 can be replaced by a comma to avoid having a run-on phrase. For example, 中共中央总书记兼国家主席兼中央军委主席习近平 is hard to read, 中共中央总书记、国家主席、中央军委主席习近平 break up this long-phrase neatly, make it easy on the eyes thus easier to read
I believe, the word 兼 is used to connect two things that are of the same status or importance
Typically, the order on a list of titles either 1. from the more prominent to the less prominent 2. following a timeline
好丈夫兼好父親 - Since one should become a husband before he becomes a father, we list them in this order, and link them with a 兼 (short phrases don't need to be broke up with a comma like the long ones)
店主兼主廚 - The owner appoints the head chef of his restaurant, therefore, 店主 comes first and 主廚 comes second in this phrase. Notice 'Owner' of a restaurant is also the more prominent status than the head chef of a restaurant, it is another reason for 店主 comes before 主廚. And '他是店主兼主廚' is a good example of not replacing 兼 with a comma -- '他是店主、主廚' sounds disjointed
You have to have a 本職 before you can find a 兼職. Therefore, one's 本職 is always listed before his 兼職
From '中共中央总书记兼国家主席兼中央军委主席习近平', we know 中共中央总书记 is the most important title 习近平 currently holds