If you take a B 737 at 50 ton its impossible to choose a V1 that would make the balanced TOD equal to a TODA in case of a 4000 m runway.
The error in your reasoning is that you mix the actual performance calculation with the runway characteristics.
Calculations are done for each temperature at max available thrust for the prevailing conditions until the highest weight is found with an associated V1 that balances the associated TOD and ASD.
After this calculation is finished it is compared to the TODA and ASDA, these distances may very well be much greater than the calculated TOD and ASD for the limiting temp and thrust. As a consequence you have a balanced take off were TOD < TODA and ASD < ASDA
Ref: Dr Prof JJ Ruijrok Delft University Section Design and Flight Mechanics research in Aircraft Performance, Propulsion and Noise.