It is worse.

If the living partial liver doesn't take hold, it dies off and becomes necrotic, and would need another surgery to take out or it'll become necrotic and they'll die of sepsis. It's also unlikely they'd survive such second surgery, due to the already existing liver failure + first surgery trauma.

In this case, you'd be asking doctors to directly kill the patient in a more painful way for a very tiny chance that it may save them, on top of if they do survive, assuming they don't relapse into alcoholism and die anyway. All while technically injuring someone else (the live donor).