From Deepak Chopra (a Hindu rather than Buddhist view of types of karma): "The Vedic seers made distinctions between different types of karma. The first type is called sanchita karma. This constitutes the entire database of all our past actions. And because the seers did not look on human existence as limited to one physical lifetime, they understood sanchita karma as the vast stockpile of karma that encompasses countless lifetimes in our past.
The second type of karma, prarabdha karma, is the particular actions that are programmed to be experienced in this lifetime. Prarabdha karma is actually a subset of sanchita karma in that it represents a small fraction of the karma from the pile of sanchita karma that is activated and ready to be experienced during the span of a lifetime. ....This is the part of karma that feels like fate and determinism.
Kriyamana karma is action that we create in the moment. It is the choices we make in our life now.
... Agama karma is the action of planning in the future. It is about the goals and intentions we have for what we want to happen in the future. Both kriyamana and agama karmas are actions that represent our creativity and it is the action feels free and undetermined." From Reference
I don't think 'instant karma' of the type you refer to is the only kind, nor that Karma is only manifest in the acquital of actions, and I think it is extremely condescending to attribute the traditional understanding of karma to the "primitive nature of early peoples".
Also I agree that 'desire' in the sense of autonomic desire for sustenance, and even very many of the less basic desires that we humans have, are quite necessary to existence. But translating the word 'TRSNA' simply as 'desire' is misleading too. It needs to be understood in the context of Buddhism as a renunciate philosophy. This is a different perspective to 'what does desire mean to me?' The renunciate has a different frame of reference to the 'worldly person'.