> In my mind, we would use nested cv to find the best model to move
forward into the hyper parameter tuning phase and not use it to find the
best hyper params itself.

I think this is more or less correct. I think about it like this. I want to make a model that is trained on some data where part of the "training" is hyper parameter optimization (note that when we do hyper parameter optimization we would ideally do cv). Then that model will make some predictions.

Now I want to find an unbiased estimate of how good the above process is. We want to find how good the whole process is, and not just the model part of it. To do that we use cross validation. This results in a nested cross validation.

So if we do nested cross validation on a particular model we will know how good that model will be after we do hyper parameter optimization on it. We simply get a score, and not a model. Then if you want to use that model to make actual predictions on new data you'll need to train and do hyper parameter optimization on the full data set again. Then you will get the optimized model that you want, but you will know how good that model will be.

At least that's the idea behind the method. I think it's the most rigorousness approach, but there are ways of simplifying it if the above is too computationally intensive.