I ithought Lyra and Pan were more cuddly and together when they were telling Asriel about nearly being cut, than they were in the actual situation.
Yeah. I think that as for me, when I read the scene in the book what stuck with me is Lyra and Pan desperately rushing back together, can't get physically close enough together even if they'd tried, them whimpering over and over and swearing "Never, ever, ever" they'd let it happen (in relation to them being separated), sobbing and both are utterly bereft at being so.close to falling victim of this awful crime and losing each other in the process.
It didn't translate well on TV as after their release from the cage, Pan was almost an after thought to Lyra because she was so focused on Mrs Coulter. (If I was helpless and witnessing my child being seconds away from some awful, awful catastrophe but was saved in the last moment, hell no would I ignore that child in favour of the firefighter who averted the danger!
)
It must be the show's budgeting, I reckon. Just too complex and expensive to animate the daemons in this way.