Netting would cause a lot of problems for maintenance people and wild life of many kinds. Birds, squirrels, etc. can get tangled in netting.

Gardeners need to be trained to leave an area in proper shape, even if it takes a little more time.

The problem of keeping mulch in place on a slope is as old as the use of mulch in the landscaping. It's an annoyance but really can't be resolved by netting. Again, this is a maintenance issue and a rake is the best tool.

Good point, I hadn't thought of the birds.

If those "gardeners" are doing things you do not want them to do, and you are paying them to do that, you need to tell them what you do not want them to do as well as what you want them to do. Then if they do not do that you fire them and hire someone that will. Your "gardeners" have been ill trained.