Dear Andrew,

       Thank you for this interesting question.  I have a few things for you to consider:

Do you want a lush lawn?  Groundcovers and native grasses will add interest to your yard and help you deal with some tricky lawn issues, but they may not be  what you want for your entire lawn.  Most native grasses grow taller than we typically like our lawn grasses to be.  Some groundcovers, though pretty and useful, may not handle heavy foot traffic.  I am not quite sure what your goal is for a "thicker" lawn. Perhaps a look at some of the resources that I have included will help you to better define your question.  Feel free to reach out with more questions.

For a healthy lawn, this article should prove useful: Spring Lawn Care | Illinois Extension | UIUC

For a quick look at some descriptions of native grasses you can take a look at these links:

Landscaping with native grasses | Illinois Extension | UIUC

Native Grasses and Flowers for Ohio Landscapes | Fairfield County Master Gardeners (osu.edu)

More on natural or native landscaping can be found in this Penn State article

Neighborly Natural Landscaping in Residential Areas (psu.edu)

And finally, here is a bit about  the use of groundcovers:

Groundcovers | University of Maryland Extension