My cat bit her tail and now my vet says it needs to be amputated.

My cat came back from the groomer not recognizing her thin tail, kept trying to bite it but never did. Honestly we thought she was just being silly. 3 weeks later I come home to blood everywhere and my poor baby freaking out. Emergency vet told me this is uncommon but it happens. She bit the tip of her tail so hard she needed stitches. We put a cone on her and watched her closely. 2 weeks later she bites it again just enough to open the stitches. She’s been at the vet for 4 days, they’re changing her bandages etc. I just received a call now that her wound is not granulating. Basically her wound is not healing because there’s not much tissues at the end of tail?The vet said we have to cut it entirely and the tail is basically useless. I’m so scared for her. Please advise me.

Edit: thank you everyone. I am in no way underestimating or doubting my vet judgement. Just a desperate attempt to hear my cat will be ok. Will be proceeding with the amputation.