I have looked into getting some greenbacks, and I keep hearing about cone breakup. My question, is it desirable? Any examples of what it might sound like?
yeah lots of examples. cone breakup can be preferable, depends on personal taste.

cone breakup (or rounding) usually makes a tone 'bigger' sounding, sounds awesome on clean and barely overdriven amps. but when you start slathering on the gain the tone from a rounded speaker gets heavily muddled and definition of signal is lost.

so the basic rule is, older rock with clean to just dirty tone uses alot of speaker breakup, modern high gain usually goes for way over rated speakers to avoid breakup cuz they want the slack tunings and distortion to keep their composure and not poot out.

examples, umm anything from 60's? hendrix, led zepplin, the who, even 70's stuff like black sabbath and AC/DC.
punk isn't dead, it's always smelled that way.

"A perfection of means, and confusion of aims, seems to be our main problem."
Speaker distortion is wonderful for rock and hard rock.
Everyone is entitled to an opinion.

Feel free to express yours so I can make an informed judgement about how stupid you are.