I like the look of sparse grass under big trees, so I think this is probably one of those "in the eye of the beholder" issues. A neighbor in the next block went a bit insane last fall and cut down several very large healthy beautiful red oaks because he was tired of the acorns. The neighbors were appalled, and his yard looks really strange now with the things he has put in the place of the trees.
I think if you simply rake up the acorns, then scatter an attractive landscaping mulch over the ground, you'll have a nice looking area and the mulch will help keep the soil in place, the biological activity healthy, and make pickup of acorns easy. If you plant a ground cover then either you have to pick the acorns out of it or let them grow where they land if the squirrels don't relocate them all.
There are ornamental grasses that will grow in the shade, but you want to be sure that when you put it in that the needs of the grass and the needs of the trees won't clash and harm the trees or compromise the investment in the grasses.
_________________ Northwesterner
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