High traffic, shade, soggy and a drainage problem. Grass will not grow here and continuing to put high traffic on soggy soil will result in compacted soil where nothing will grow.

Suggest that you fix the drainage problem. If not fixable, then can you build a stone dust or gravel or stepping stone path for the high traffic area?

Instead of mowing beside the sidewalk, would a low growing ground cover work?

moss.

froggy

Thanks for the suggestions.
I improved the drainage problem a lot by diverting the flow of an intermittent spring away from the area and cleaning out a nearby drain but still get a fair amount of water in the area. The high traffic/soggy area is supposed to be a mini-playground. I don't know why it is receiving so much more water as of late. Maybe neighbors did something to increase runoff? Maybe damage to tree canopy did it?