Conservation agriculture (CA) allows farmers to reduce costs and enhance soil health, but tends to increase weed infestation and associated crop yield loss, and/or herbicide use. We investigated how much tillage reduces weed infestation and yield loss, and which systems and weed species are the most affected by tillage suppression. We collected farming practices on 395 arable cropping systems mainly from France, and simulated them over 30 years and with 10 weather repetitions, using FLORSYS. This process-based model simulates daily multi-species weed floras and crop canopies from cropping systems and pedoclimate over the years. Three series were simulated, (1) using the recorded systems, (2) eliminating tillage without any other changes, (3) eliminating herbicides without any other changes. Each series was run twice, once with a regional weed-flora pool to simulate weed dynamics and their impact on crop production and biodiversity, and once without weeds to predict potential crop yield. Among the recorded systems, herbicide treatment frequency index (HTFI) averaged over rotation increased when tillage frequency decreased. No recorded no-till system was herbicide-free. The untilled crops with the lowest HTFI (0.16) were unusual crops, i.e., relay grass-crops or multi-annual crops. Simulations of the recorded systems showed no correlation between tillage-frequency, and weed biomass or weed-caused yield loss. When tillage was deleted without any other change, yield loss almost doubled. We identified (1) which weed species and traits (e.g., spring annuals) increased after tillage suppression and in which cropping systems, (2) which recorded systems were robust to tillage suppression in terms of yield loss (with cover crops, summer crops, etc.), (3) which no-till systems (recorded or obtained after deleting tillage) limited yield loss (e.g., with frequent and/or efficient herbicides), (4) which management techniques were associated with a reduction in tillage, in herbicides, and in yield loss (long and diverse rotations, cover crops, etc.). No tested system achieved all three objectives simultaneously. The simulations indicated that two CA pillars (diverse crop rotations, cover cropping) were essential to manage weeds while reducing (or eliminating) both tillage and herbicide use. More no-till cropping systems must be investigated to determine whether sustainable no-till herbicide-free systems are possible.