Why is convolution filter used instead of correlation filter in CNN?
Convolution (as a term) matches with what we are trying to do in a CNN: we are building a (sort of) filter to extract certain feature from a signal. What is the output of the filter when a given image (vector) is given as input? Best thought of as convolution between the input and the filter.

Correlation (as a term) would be preferred when we are dealing with two signals/inputs. Probably bit misleading applied to CNN feature extraction operation.

I think this is more to do with terminology. The magnitude will be same as you suggest. Flipping happens because convolution is generally calculated after flipping the filter vector representation.