Need to remove old copper sprinkler system before installing new PVC one?

We bought a house last year that had copper pipes for the sprinkler system (and the gas line in the yard.... I know). There are quick a few pretty big leaks in the system. I've had a few friends say it's probably just better to start over with a PVC system. I'm trying to figure out if I need to actually remove all the copper pipes, or if I can just install a new PVC system over it.

Any thoughts here? I was going to rent a trenching machine for a day but I'm not sure if it's safe to trench with the copper pipes in the ground, or if it would just cut through the copper. I'm trying to avoid having to manually dig up all the copper and then install the PVC.