Many farmers do exactly that. Depending on crop being planted next they do not even till previous crop, just drill in new seed. Next time you drive out to family spread watch for wheat stubble from last summer standing in green field of 3" tall wheat.
This is what we do. After everything is harvested I do a "light" disc to tear everything up, usually sometime late Sept. I leave it alone to start decomposition, add moisture if needed. Sometime in Oct I will add compost and or fertilizer and disc heavily if decomposition is slow or turn over completely if good decomp. As soon as frost is gone in spring or late March I disc heavy again and turn again. Process is alot of effort but is turning the horrible clay into soil that is easier to work by hand and requires 1/3 less water.
We hope to start this year(next year realistically) providing all fresh vegetable produce for 5+ families consumption each year and some to take to farmers market to generate enough revenue to offset costs.
ETA - I won't win any awards for soul conservation. Too much tilling.