This comes up a lot on the forum (Re: ADOBE DRAW TO ILLUSTRATOR CC PROBLEM (MILLIONS OF ANCHOR POINTS).
You haven't done anything "wrong." Unfortunately, though, there is no way to change the way Draw strokes export to Ai; strokes in Draw are like an Illustrator blob brush, so they do send to Illustrator as "shapes" and the only way to get a simple/single path down the middle of strokes is to redraw them.
As I've mentioned in other posts, I don't know whether a change is being considered but I do pass all of these comments along to the product team so it's aware that the way strokes are handled can be problematic for people (especially when they're using Draw for the first time).
I know that's probably not the response you hoped for, but I hope the knowledge helps.
Thanks so much Sue - after I posted my question I did stumble across a few other threads which made me realise what was happening! I will just have to live in hope (like thousands of other people) that the powers that be create a way to draw lines which can be exported to Illustrator - it's seems like a simple thing but I'm sure it isn't!! Oh well! At least I now know I'm not just being stupid, lol!!
Oh good. I'm glad you got your answer sooner rather than later.
Like I said, it does come up a lot so I do appreciate it when people post about it because it gives me another opportunity to bring it up to the product team.