My asparagus crowns are well below what most tillers reach, but your spears likely were pretty severely pummeled. Wait a few weeks before you throw in the towel. Do you have records of when you started to harvest from previous years? That will give you a rough estimate of how close the spears were to breaking soil. If your winter was like most of the east coast, you may need to add a few weeks to last years' date. I hope you told your tiller guy he won't be coming back next year. He could pay for the plants, but losing 3 years is gonna hurt.

Catherinet makes a good point - caps can be easier to read when someone has vision issues. Many plant stems will continue to grow after cutting. And you can most certainly grow new green onions from the cut-off ends if there are still roots attached. I've done it myself. That's how I got my lemongrass, years ago. I also grew a cabbage plant from a store bought head that had roots sprouting from the base. I cut out the core, planted it in a container, put it on a sunny windowsill, and it put out new leaves - no heading tho. I've also done the same with celery. If there's enough of the root 'plate' still attached, and it's fairly fresh, it can put out roots and grow. Here's what the cabbage looked like. Unfortunately, it died off after I transplanted it outside - I think because it was too hot and humid.

Yes worms have no issues eating asparagus. I have added the tough uncooked ends multiple times to my bin. I will warn you it can smell a bit if you leave them on top so I recommend burying them in the bedding or castings. Similar things happen with broccoli as well.

Like Jack said adult beetles come out of the ground when the spears emerge. If all the spears are harvested you may find adults sitting on the top of a spear looking for mates. If a spear is allowed to grow and fern out the adults will find it and congregate for an orgy, and the best place to hunt them down early and reduce the population.