I planted 10 asparagus crowns late last summer. All 10 came up. I was told to let them grow and not cut them the first year. They are bushed out and falling over. There stalk is half the size of a pencil.
Some plants have a new chute growing beside the existing stalk.
If you want to clean up the stalks that have broken it really shouldn't be a problem for the plant. A friend of mine would like information on purchasing white asparagus root. She wishes to grow it. How this is done is by keeping the spears buried under dirt until large enough to cut. We grow, for the most part, UC157 variety which is the most widely used commercial variety grown here in California.