The issue of the wolf and the lion… after all, these are constants

I don’t remember anymore. From what you describe, this ties in with the Rif’s, Maimonides’, and Damhon’s explanation regarding the exemption of the Rabbi in the Barahar and perhaps also the exemption of the Keren Tema everywhere. The explanation is that the owner of the animal has permission to walk in the Barahar and the one who causes the damage must be careful. This does not exist with cheetahs. There is no permission to walk with it in the Barahar. Incidentally, the permission to walk in the Barahar is not conditional on it being tied and guarded. On the contrary, the animal walks there alone and yet the person is exempt. Therefore, we are not talking about someone who went out with their beloved cheetah for a tour in the Barahar, but rather about someone who sent their beloved cheetah to walk there alone for the joy of the public.
Even in our places, it is accepted that there is no legal permission to raise animals that are not dogs or cats, especially dangerous ones. After all, even in his own home, there is a prohibition on a bad dog (although it seems that this is a prohibition and there is no obligation to pay damages, and this is simply because it is a place of my permission and therefore the duty of caution is still on whoever enters there).