Yeah, the single flip control - as you said - technically does not change the family.
Still, it would be better if it had the ability to track them with a yes/no parameter. You never know when it might come in handy. Just let the end-user decide.
I agree this would be very helpful, but there would need to be a way to prevent a family from being mirrored using the mirror tool for this to be reliable.
@mhiserZFHXS agreed, The mirror command should just be able to push what it did to the family and update the parameter. The other option would be to be able to also track if the family was flipped using the command. This way you could track both the mirror command and the flip control and compare.