I think this comes down to two things: first, they didn't have a third solid story arc from Thomas Harris to make another movie after this one. Aside from the prequel idea for Red Dragon. And Anthony Hopkins was getting too old and obese to make another convincing appearence, well until he lost weight for Red Dragon. So they thought this is it, this is the end of the line, let's end with a flourish, a dramatic gesture, self-sacrifice to show that yes, he was capable of truly caring about other people, about Clarice anyway.
Honestly though, I didn't like it either. I love Hannibal Lecter and I would much prefer him to have use of both his hands. I have so much sympathy for the guy and how hard it is for him to function normally in a world full of insipid, horrible, self-centered pricks.

Also, couldn't he have hawked at the chain?

PSI didn't mean that YOU are idiotic, nor your opinion, just that I think it was an idiotic way to solve a plot problem!

That's still idiotic. It doesn't take that long to pick a lock if you know what you're doing. Handcuffs have a little spring that pops them open when you hit the right spot in the lock, which is why the handcuff key is such a simple one. We saw in SOTL that he can pick a lock very quickly.

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It makes no sense, in "The Silence" he uses a small piece of wire to break
free from the hancuffs but here, in a kitchen full of cutlery and pointy utensils,
decides to play the fool?. The good doctor is losing his abilities.

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