Why Use Conceptual Models

It is important for students to begin learning how to develop conceptual models of how things work for several reasons:

Development of conceptual models is first step in developing more detailed quantitative models.
Interactive development of conceptual models can be used very effectively as an Interactive Engagement learning environment. See Modeling Methodology for Physics Teachers (more info) .
For some topics, having students participate in the development and validation of conceptual models to help them understand different physical processes is a worthwhile learning objective.
The development of conceptual models can help introduce students to the terminology and to a conceptual understanding of systems thinking and modeling. For example, positive and negative feedback loops can be qualitatively discussed and identified with causal loop diagrams. The development and use of causal loop diagrams can help students shift from linear thought processes to systems thinking.

When is it advantageous to use conceptual models?

When introducing a new topic in class regardless of whether the ultimate goal is to develop the topic qualitatively or quantitatively.
When equations for some process being studied seem to obscure student understanding it is a good idea to step back a bit and discuss a conceptual model of the processes. Actually, it is typically best to develop a conceptual framework for understanding before introducing equations.
To help explain and discuss interesting features in data sets.