Currently, most intersection models embedded in macroscopic Dynamic Network Loading (DNL) models are not well suited for urban and regional applications. This is so because so-called internal intersection supply constraints, bounding flows due to crossing and merging conflicts inherent to the intersection itself, are missing. This paper discusses the problems that arise upon introducing such constraints, which result firstly from a lack of empirical knowledge on driver behavior at general intersections under varying conditions and the incompatibility of existing theories that describe this behavior with macroscopic DNL. A generic framework for the distribution of (internal) supply is adopted, which is based on the definition of priority parameters that describe the strength of each flow in the competition for a particular supply. Secondly, using this representation, it is shown that intersection models even under realistic behavioral assumptions and in simple configurations (i.e. without internal supply constraints) can produce non-unique flow patterns under identical boundary conditions. This solution non-uniqueness is thoroughly discussed and conceptual approaches on how it can be dealt with in the model are provided. Also the spatial modeling point of view is considered as opposed to the more traditional point-like modeling. It is revealed that the undesirable model properties are not solved but rather enhanced when diverting from a point-like to a spatial modeling approach. Therefore, we see more merit in continuing the point-like approach for the future development of sophisticated intersection models. Necessary research steps along these lines are formulated.