RaMBa"M's "Wondrous Point" about cooking "treif" meat from a Kosher animal with milk undermined by a simple Gemara?

Question

Beitzah 12b seems to undermine RaMBa"M's Nekudah Niflaah that cooking and enjoying (not eating) Basar Tehorah Neveilah with milk is Mutar.

Beitzah 12a-12b has R' Yohanan appalled at the suggestion that someone who cooked Gid HaNasheh with milk on Yom Tov and ate the product is given five separate sets of lashes:

1. Cooking Gid on Yom Tov (there's no purpose for the product, since it's not Kosher, so there's no Ochel Nefesh).
2. Eating Gid.
3. Cooking meat and milk (not specifically on Yom Tov; just the general prohibition against cooking such a mixture).
4. Eating meat and milk that were cooked together.
5. Burning on Yom Tov (see 1).

He responds with shock and dismisses all the Yom Tov cooking violations because of Ochel Nefesh. But he doesn't say he's exempt from the lashes of cooking or eating meat and milk together.

Doesn't this undermine RaMBa"M's point that Kosher-species meat that is unKosher for other reasons is exempt from the added prohibitions of meat/milk mixtures?

Answer 1

The Rambam never permitted cooking Nevelah meat with milk. He only permitted deriving benefit from the mixture. Cooking Nevelah meat with milk is still prohibited (Maachalot Asurot 9:6).

Answer 2

Firstly, one must distinguish between Gid Hanasheh and Achilat Neveilah. Secondly one must distinguish between the Nekudah Hanifla'ah and the principle of Ein Issur Chal Al Issur. Finally we must deal with why the principle of Ein Issur Chal Al issur doesn't apply when cooking the Gid Hanashe with milk. This final question strikes me as extremely interesting.

Gid Hanashe is a nerve found within the hindquarter of a kosher animal, while a neveilah is an animal which has not been killed with a kosher shechitah.

The principle of Ein Issur Chal al Issur states that once something is prohibited, additional reasons for prohibiting it do not take effect. The Nekudah hanifla'ah says that milk and neveilah isn't an exception to Ein Issur Chal al Issur despite the fact that it seemingly falls under the category of issur mosif. This is explained more thoroughly in the link you provided.

The reason Gid Hanasheh is prohibited to mix with milk despite ein issur chal al issur is in my opinion due to the fact that Gid Hanasheh has a Tzvei Dinim (dual nature) of being both meat and Gid Hanasheh. Although the prohibition to eat the Gid Hanasheh is already in place at the time of cooking the meat with milk, since any meat which wasn't part of the Gid Hanashe would become "treif" through the cooking process, we can apply the principle of Issur Kolel (Issur Kolel What is it?) to extend this new prohibition to even the Gid Hanasheh.