What's the difference of calculating features directly vs having a CNN interpret it?
what if my data is such that I can interpret, whether it's of a certain type by doing direct measurements on the data?


I love machine learning as much as the next guy, but if there is a known way to map your input to your desired output, you should use that, period.


Or perhaps it's that CNN becomes viable when there are so many measurable parameters that trying to infer all of them by manual algorithm becomes laborious?


If speed becomes an issue, then indeed, you may need to consider alternatives, including training a model. There are indeed situations where a learned function may be a bit more simplistic, but good enough and faster than an exact algorithm.

However, these scenarios are quite rare. Inference with neural networks may require non-negligible computational power, so I would guess that in most situations, the exact algorithm will be faster regardless.