Egg shells are good for growing grass as long as you put them in with the soil when planting new grass seed.
However the egg shells may do more damage to the grass when you just sprinkle egg shells onto your grass.
For the grass to benefit from the egg shells they need to be mixed in with the soil.
Also egg shells are great to add to your compost pile and then you can use the compost with the egg shells to grow plants and also grow vegetables as well.
The egg shells add nutrients and minerals to the plants soil so that the plants thrive much better.
After I started adding egg shells to my compost pile and then began using the compost with egg shells in my garden my flowers and other vegetables have grown faster and they have thrived better too.