I never heard of any Gezeira for a Sakana. I guess the Chachamim understood that it’s something you’d care enough about on your own to be careful. What would they have done in our self neglecting generation?
Where do you find that a person is Treif? Surely, you may not eat one, but not that it’s Treif. Think about it: Your tongue is in your mouth for over 24 hours. What do you do about that, wrap it in paper?
We see that a live animal is not food from Hilchos Tumas Ochlin. There are probably more instances to point to which are not on my mind right now, but it is a very strong Svara.
More to the root of the issue, Your hand doesn’t get cooked. Although you can argue that meat doesn’t either cook in a fraction of a second, Kach Shiurei Chachomin. Also, dead meat is inert, giving room for the concept of K’dei Klipa. Live muscle has circulation of blood and works together.
Ever Min Hachai is dead meat by the time you are eating it.