I think it would be easier to just accept that "model" already means "simplified description" (source https://en.oxforddictionaries.com/definition/model) and use another word to refer to the superset you're mentioning.
That's because language is mostly useful for communication between people, here and now. Treating a natural language as a construct to refine until it reaches a mathematical beauty where nice and short words mean what they "should mean" often causes so much grief and wasted energy.
Or just call it a simplification instead of a model. It's a subset of all models. Alternatively, an explanation of it captures all the detail.
Model is combined with another interesting word, essence as in essential, which is what it's supposed to capture, for given purpose.
If the purpose of the model is explanatory power and accuracy, these two do not necessarily form a one dimensional trade-off.