Especially ironic when suburbanites rave about how houses are infinitely better than apartments because they’re “closer to nature.” You want to be closer to nature? Let natural processes work and have a lawn of whatever grows in your area naturally (even an “invasive” species is better than lawn grasses, unironically, and lawn grasses are almost always also non-native species, just ones that can’t actually survive in the environment.) Don’t water, don’t mow, don’t fertilize, just let nature do its thing. It will also attract more pollinators, birds, wildlife in general and instead of a lawn, soon you’ll have a natural meadow in your yard. That’s nature, a lawn that needs excessive water, chemical fertilizers, and poison just to maintain isn’t.
Yes, you would have to densely broadcast seed/plant plugs with native prairie species or noxious and invasive stuff will take over initially. And you would have to kill all the grass, either with a spray (which helps keep the existing invasive seed bank down), or till or sod cut or solarize or smother the grass.
If you replant relatively quickly, erosion won’t be too much of a concern as the natives will establish fast enough to stabilize the soil. Long term, the natives will actually reduce erosion compared to lawn grass. You don’t need to burn in an urban setting, mowing once or twice a year (once in earlier spring and maybe again in early summer to help natives out compete invasives) is gonna be enough generally.