Why was the lack of a formal system of succession a problem in the Roman empire?

Answer 1

It is not altogether true that a system of succession never existed. Within the Julio-Claudian family there existed a settled tradition that sons (and if not available, other near relatives) should succeed. If you'd check under 'family tree of Roman Emperors' in Wikipedia, you will see that many emperors belonged to family trees where succession went along the same lines and did not lead to national unrest.

The problem mainly was that so few Emperors died peacefully in their beds; a great number was murdered for not living up to expectations, certainly in the later years of the Empire. A formal system of succession would have been of little use in these cases: if you murder an emperor, it is not a clever idea to allow his son on the throne who will want to revenge his father by having you executed. Or allow an established "succession commission" to appoint someone not sympathetic with your actions.

In those later years, the often violent death of an Emperor usually led to a power struggle amongst his murderers, while at the same time one or more armies in the provinces declared for their commander as the new emperor. This invariably caused a lot of civic unrest each time it happened. It also precipitated the loss of control over provinces as armies who were trying to see their commander on the throne lost focus on the job they were supposed to do in their province: keeping order and keeping out any tribes trying to get in.