Discing weeds is an efficient way to take them down (if tall and thick) to clear trails and field edges.
Unfortunately, if you want to establish grass....you'll hate yourself for discing a field for that purpose.
Weed seeds lie dormant in the soil for years and years and LOVE disturbed soil. You'd be trading one type of weed for several others and typically weeds outgrow grass.
Once grass is established and gets thick enough it will choke out a lot of other undesirable vegetation. But in your case, spraying is the answer.
Your logic was not bad.....it just doesn't play out that way in reality.