I agree. I have seen animals recover from horrendous wounds, horse legs degloved by wire with tendons hanging, dogs put through surgeries that left them permanently crippled living at the vets for months, many tough things. I've insisted on keeping some alive myself that suffered.
I feel that everyone has to make the best choice they can at that moment. Emotions color our vision and make it so hard.
But truly after seeing one horse in particular suffer so awfully, trembling and sweating for days through the pain meds, sitting down like a dog in exhaustion, I've learned something. The woman who owned that horse had been warned repeatedly that he was going to get hurt due to his studdy behavior in the pasture. She was jealous and hateful to the person who warned her so persisted. So when her horse was found hanging in the fence by a leg that was nothing but bone after being left unattended for hours, she just had to "save" him. Because of her guilt. It wasn't love, just ugly guilt that matched the emotions that made her leave him out day after day adjacent to mares he was trying to get to. He suffered horribly so she could feel better about being a jerk. It was truly inhumane. Sure he's alive today and can walk, after a fashion. But those ends didn't justify the months of agony.
Animals don't reflect about the years they will miss but they sure feel pain. It's not right to make them suffer to make us feel better. All we can do is make good choices and you did that well. Better than many. Better then I've done at times.
Good job being so giving to your beautiful hen and sending her on her way. I don't know if she could have recovered but your instinct was likely right. Be at peace.