DRY is good but like any abstraction it has tradeoffs. It might give you a warm feeling to do the refactor, but you might end up with code that's harder to understand and harder to replace.

I've always found the https://en.wikipedia.org/wiki/Open%E2%80%93closed_principle, where you derive from classes instead of editing them in-place, sort of appealing for this reason.

What is this implying? That instead of adding a property/method to a class you should instead create a child class that inherits from the original with the new properties? Sounds like a great way to have a very complicated class hierarchy IMO

Exactly that. Just because you want new behavior doesn't mean all the other consumers of that class also want it. The old behavior should still exist, and have a name. I'm not sure whether the idea was ever fully developed into patterns for replacing deep hierarchies with simplified classes that factor out some inheritance from otherwise-unused base classes.

Prefer extension via composition for more flexibility than via inheritance, which tends to create overly rigid hierarchies.