Why do egg white cartons warn that pasteurized egg whites shouldn’t be used for whipping or meringue

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 nature of meringue: they will start to fall apart as soon as you stop whipping. There are a few tricks to help it hold longer, but in general you want to have EVERYTHING ready to go as soon as the meringue is whipped.

To help stabilize the meringue you can:

• Use a copper or SILVER-plated bowl to whip, or add a tiny amount of powdered copper supplement from a health food store
• Acidify it slightly: add 1/8 tsp cream of tartar or 1/2 tsp lemon juice per white, before beating
• Let the bowl warm to room temperature, which increases the ability of the whites to take in air
• Ensure there is absolutely no yolk in with the whites. The fat greatly destabilizes the foam.

Now for WHY these tricks work:

I'm going to quote heavily from Harold McGee's "On Food and Cooking", as it does a wonderful job explaining meringues and other whipped egg whites:

Like the head on a beer or a cappucino, an egg foam is a liquid--the white--filled with a gas --air-- in such a way that the mixuture of liquid and gas keeps its shape, like a solid. It's a mass of bubbles, with air inside each bubble, and the white spread out into a thin film to form the bubble walls. And the makeup of these liquid walls determines how long a foam can stand up. Pure water has such a strong surface tension--such strong attractive forces among its molecules--that it immediately starts to pull itself together into a compact puddle; and it's so runny that it puddles almost immediately. The many nonwater molecules in egg white both reduce the surface tension of the water they float in, and make it less runny, and thus allow the bubbles to survive long enough to accumulate in a sizeable mass. What gives the mass of foam a useful kitchen lifetime is the white's team of proteins.

Whisking unfolds these proteins, primarily globulins and ovotranferrin, which bond to each other and stabilize the bubble walls. Cooking will evaporate the water and unfold ovoalbumin, creating a rigid and permanent protein network.

However, the same proteins can ALSO destabilize the foam if they bond too tightly. "The protein network begins to collapse when too many of these bonds accumulate and the proteins cluster together too tightly" (page 102). In the case of egg proteins, one of the strongest bonds is a disulfide bond between the sulfur-containing amino acids, cysteine and methionine. Eggs contain copious quantities of these amino acids, which are why they produce such a potent stench when they spoil; the sulfur is converted to malodorous sulfur compounds, particularly hydrogen sulfide.

Copper, silver, and acids stabilize the egg foam by preventing the formation of these disulfide bonds. To quote Harold McGee (page 103):

It turns out that along with a few other metals, copper has the useful tendency to form extremely tight bonds with reactive sulfur groups: so tight that the sulfur is essentially preventing from reacting with anything else. So the presence of copper in foaming eggs whites essentially eliminates the strongest kind of protein bond that can form, and makes it harder for the proteins to embrace each other too tightly.

McGee also notes that silver has the same property of inhibiting disulfide bonding. Acid achieves the same goal of reducing disulfide bonding, but works slightly differently:

The sulfur bonds form when the sulfur-hydrogen (S-H) groups on two different protein molecules shed their hydrogens and form a sulfur-sulfur (S-S) connection with each other. The addition of an acid boosts the number of free-floating hydrogen (H) ions in the egg white, which makes it much harder for the S-H groups to shed their own H, and so slows the sulfur bonding down to a crawl.