The purpose for these "drainage ditches", is so that water can flow freely, during naturally occuring disasters such as during a Hurricane & torrential downpours, so that deluges an inundations don't "flood" your home. Water, needs to have -some- place to drain off, & away from your home, possibly, eventually leading to a waterway...so it can continue to flow, unobstructed "downstream."
Before digging in one's own yard, in Virginia, you must notify Dominion Power, ahead of time, in advance, so they may mark your yard, for locations where underground , utilities, like gas water electric , that supply, your services, even if it's underground 'cable' for internet, etc..Your laws & City Codes, may vary, from the Commonwealth's, but if I were you, I'd be looking it up for your County, at minimum, so you know, prior to doing anything.
Have you asked a single neighbor, why, it appears no one has yet to plant any trees in their front yards yet ?
Because, it looks to me, as if there are no trees in the front yards, at all & quite possibly, there's a reason...