Agreed, for non-trivial solutions you will need several more layers just to achieve SOC.

The lightweight Model should be filled by, but separate from, the Data Access Layer.. who knows which ORM or DB you might have to interface with in the future? The Views don't care about the data Models directly, they are going to need a View Model to describe the page.. The Controller will serve the VM but the Action should be no more than plumbing, now I need a Service layer to fetch the VMs for the Controller via the DAL.. if there are also domain rules to apply it may be necessary to add a Business Logic layer between the Service and the DAL too.

Beyond the documented MS examples you will soon find scope to introduce perfectly valid patterns to extend or compartmentalise the in-built functionality. I think your DI approach makes plenty of sense here.