I've tried checking different extension websites on this. Most don't mention it directly. I did find this on Virginias's site. It's the only place I could find any explanation "why".
Do not allow any small spindly spears that are not marketable grow into ferns while your harvesting. If this is allowed to happen, this provides and excellent site for asparagus beetles to lay their eggs, change into larvae, and into adult beetles. The field should look absolutely clean during harvest, except for new spears coming up or ones ready to be harvested.
I did read a few places that harvesting it once it is established causes more bud development for the following year, but that did not mention harvesting clean. I'm not going to jump to a conclusion on that.
I harvest mine clean, even those skinny spears. They cook pretty fast but taste as good as the others. That doesn't mean my way is the right way or best way, just the way I do it.