There would then need to be ladders over most of the surface of the chimney, and with the anchors for the ladder mortared into the chimney, and the whole point of climbing the ladder in the first place is to repoint the mortar, you couldn't rely on the anchors being sound.
What material wouldn't degrade over the lifetime of the chimney?
Steel... just like via ferrata. These chimneys aren't more than like 150 years old max.
Maybe. I don't know. I've seen plenty of old fixed ladders that have rusted to uselessness, but they weren't 150 years old.
Via ferratas are almost always embedded into pure rock, generally limestone, right? Brick and mortar is quite a bit different.