Not good for exercise, it's heavy and has telephonic effects (walking/running sound transmit through the cable). Also ties you to the audio source.

Does anyone actually make wired headphones with ANC?

Look up "bullet MMCX IEMs". Plenty of options out there for cables too, some far less microphonic than others, and you can wear them over-ear to reduce that effect even more.

No ANC but they already isolate sound very well.