Another issue is that by the time the type_id intrinsic is called, all lifetimes are already erased. This means that it is impossible to give &'static u8 a different TypeId fron &'a u8. It would only be possible to use the TypeId::Static variant for types that don't have any lifetime parameters at all.
Eq requires the relation to be reflexive, in other words it requires x == x to hold for all x. This property is why we have Eq in the first place instead of just PartialEq, which doesn't require this.