The road isn’t a better option but issues with grass in residential areas:

• Tree roots and other trip hazards
• People parking their 5 giant SUVs and pickup trucks on them (this can happen on sidewalks too, but it’s often worse)
• Dog shit that is less visible
• Road design is usually more hostile when there aren’t sidewalks since they don’t even consider the existence of pedestrians
• Sometimes it’s not grass so much as mud, particularly when flooding has occurred recently (which has gotten more common as climate change has advanced).
• Running on a sidewalk (or road) is better for reducing injury despite grass feeling softer (since it’s more uneven).

And on the larger sidewalks you can ride bikes on them relatively safely.