The Cure's legacy

That's a fair point, but did Shake it Off stick with you because it was abysmal or because it resonated with you?
I'd wager FIIL sticks with people for the second reason.

It stuck with me because I couldn't avoid it. It was everywhere whether I liked it (nope) or not.

It depends on if you are talking about their legacy from hardcore Cure fans, or just people in general (by this, I mean the regular population that knows of them but that doesn't know, say, every lyric to 'The Same Deep Water As You').

I think by the general public they will be known as a goth band that all the 'sad, depressed, bad kids' listened to in the 80s, that also had a few out-of-context poppy singles about Fridays and cats. Maybe they'll be remembered by these people for Disintegration as well. And for lots of hairspray.

But by hardcore fans (us, for example) they'll be remembered for so many things, that are also personal and not as universal. For example, I think a lot of us will remember them for times when we were in a dark place and they helped lift us out of that depression. Or maybe that's just me. They'll be remembered for persevering through a lot: quite a few changes of lineups, changes in the style of music they created, getting bad feedback from their fans when they released Bloodflowers (though it is clearly their best album). They'll have the legacy of being in, assisting in, or being a major part of our best memories. 

I think their legacy will be related to innovative song writing - there's something very special about it. The literary and classical influences make it pretty unique for me.