Does cooking nopales with a copper coin actually neutralize the mucilage, and if so, why

Yes, as mentioned previously it is beneficial to whip egg whites in copper bowls BUT it is important to note that the impact on the egg whites from the copper is primarily beneficial for applications where the final product is going to be baked. You will generally not notice any increased volume in the whipped egg whites themselves, compared to what you'd get without a copper bowl.

As the whites are whipped the copper bonds to create a copper salt that increases the temperature at which the proteins will coagulate. The copper salt makes them more pliable and able to better expand without rupturing. Under "usual" conditions (glass, stainless steel, ceramic) they will coagulate at around 160F degrees. When whipped in a copper bowl they have to reach 170F degrees before they coagulate. This means that they will have a 10 degree increase in temperature to continue to expand and increase in volume.

This also means that if you're talking about whipping egg whites for meringues, dried for cookies or other desserts, the expense of a copper bowl will not be worthwhile as you're not looking for expansion properties in these items. If you're doing a lot of cakes and souffles then a copper bowl would certainly produce better results.

This is the same question, in essence as why any of these combinations are dissonant or unexpected:

• Marina sauce on soba noodles
• Cheese on Chinese stir fry
• Haggis jambalaya

Every cuisine is a part of a culture, and there are cultural expectations for what is normal or not normal.

A deeper question would be how and why such cultural expectations develop.

Note that this is a speculation, but an informed anthropological speculation:

Every cuisine is associated with a geographic region, where certain agricultural products are prominent. The people in the area, quite naturally, learned to cook with the resources they had available. So it would be odd for a mountainous culture like Tibetans to have seafood dishes, just as it would be odd for the inhabitants of modern day Shanghai to have Yakk milk dishes.

Over time, the culture adapts and finds flavor combinations and techniques that are applicable to its resources (stir frying in china, for minimal fuel use, for example). These traditions form the backbone of the cuisine, and are how we recognize what is or is not part of that cuisine.

This allows us to make an educated guess as to why balsamic vingegar seems odd in Mexican food.

Mexico has not historically been a land of the grape, so they do not have a wine making or vinegar making tradition. Therefore, a product like balsamic vinegar is not a part of their tradition.

Balsamic is also well identified with the part of Italy now called Modena, where it would have evolved because grapes were available, and there was a wine making industry already.

Putting the two together confounds cultural expectations.

Nonetheless, there are many chef's who enjoy and practice combining foods and technique across cultural and cuisine boundaries, and thus we have the modern practice of fusion cuisine.