Why not let it fall in one piece, so it will be more intact and thus easier to investigate as to what went wrong?

There were designated areas where it was okay for Super Heavy and Starship to encounter the water per the launch license. Having them do so outside those areas endangers endangers ship and aircraft traffic. The flight termination system is there expressly to mitigate risks to those not involved with the launch.

Neither Starship nor Super Heavy were intended to be recovered at all from this test flight, even if things went perfectly. Per the Environmental Assessment Re-evaluation Super Heavy was to be sunk after landing and Starship was intended to explode on impact from mixing of the remaining propellant. There was no way there would be a forensic recovery effort after the stack lost control.

Why not let it fall in one piece, so it will be more intact and thus easier to investigate as to what went wrong?

There were designated areas where it was okay for Super Heavy and Starship to encounter the water per the launch license. Having them do so outside those areas endangers ship and aircraft traffic. The flight termination system is there expressly to mitigate risks to those not involved with the launch.

Neither Starship nor Super Heavy were intended to be recovered at all from this test flight, even if things went perfectly. Per the Environmental Assessment Re-evaluation Super Heavy was to be sunk after landing and Starship was intended to explode on impact from mixing of the remaining propellant. There was no way there would be a forensic recovery effort after the stack lost control.