Modern baking powder is basically always "double-acting". This makes a lot of sense compared to the older single-acting powder, since the gas formed during baking won't be removed by mechanical actions like pouring batter into a dish, and occurs when the starch is ready to form a gel, stabilizing the foam.
So what's the point of the room-temperature reaction? It doesn't seem like there's any particular point in producing gas immediately, compared to during the baking process.
Note that I'm looking for documented reasoning from manufacturers or food scientists, not people's informed guesses or personal opinions.
Best Answer
The main rationale for an early reaction is to help create small bubbles during the final part of mixing that contribute to the fine structure of baked goods, as well as to add balance to the rate at which bubbles expand during baking.
Details:
There are practical chemical reasons for doing this: a lot of the standard ingredients used to make simple baking powders work through a sort of staged reaction. For example, Rumford Baking Powder uses monocalcium phosphate, designed to react precisely with the amount of sodium bicarbonate to avoid changing the pH in the batter. But its action happens in two phases, using that single ingredient:
Historically, this is how many baking powders worked. The first ingredients that tended to have a stronger delayed action tended to be aluminum based, and the movement away from aluminum products in the past couple decades has led to heavy marketing of "aluminum-free" baking powders. (Some people also find that such "slow acting" formulas leave more of a metallic/chemical taste.) The "aluminum-free" powders are often based on these historical formulas, which tend to release a higher percentage of gas at room temperature.
That said, there is still a benefit to having some first action of baking powders. The main reason is to create a consistent fine-grained baked product. As Shirley Corriher notes in Bakewise (pp. 46-47):
Corriher goes on to note that liquids and eggs release steam that can also inflate the bubbles in batter, but once again, they do not create the bubbles. She concludes again by restating that "creating fine bubbles in the batter during the mixing is a crucial part of leavening."
Depending on the mixing technique, these bubbles can be created in a variety of ways, such as creaming butter and sugar together or whipping eggs. But the initial production of gas during the final part of mixing from baking powder reactions can be important in allowing these initial fine-grained bubbles to form as well. As noted here:
Note in particular the bit about air-cell nucleation produced by baking powder. That link goes on to describe other types of baking powder options and their various effects in baking, depending on how much gas is released early vs. late.
It's sort of analogous to the rationale for kneading and reshaping bread dough after an initial rise: while you can make bread without doing this, part of the degassing and shaping is about breaking up large bubbles and creating a more fine-grained texture in the bread. But you need to have gas there to begin with as you are kneading/shaping to get maximum structure (hence the need for a first rise). Having baking powder release some gas during mixing serves a similar purpose, as it expands existing bubbles but further mixing can break them up to form smaller links in the batter and create a smaller foam. Ultimately, it will lead to a more consistent structure for the interior of the final baked product.
Also, baking powders used by home bakers are generally formulated to be multipurpose. As mentioned above, many cake batters, cookie doughs, etc. will include some other way of trapping gas during mixing, but not all recipes have a step like this. While many recipes will incorporate the baking powder at the very end with other dry ingredients (and just "mix until combined"), other recipes without other methods for trapping gases might mix the batter for a couple minutes at the end to use the gas generated from baking powder to leaven the dough and create the structure of bubbles. (One similarly sees recipes that use a combination of baking soda with acid along with baking powder: again, the baking soda reacts immediately and will help to trap gases and make bubbles even if the batter is just "mixed until combined," while the baking powder will enlarge those bubbles during baking.)
And there are baking powders (mostly used commercially) that produce the vast majority of their leavening in delayed action during heating. These are generally known as "slow-acting baking powders" rather than "double-acting." For example, Fleischmann's baking powder releases only about 10% of its gas initially at room temperature and 90% in the oven (compared to most standard double-acting powders, which tend to release 30-70% of their gas during the initial action). Slow-acting baking powders are more useful for batters and doughs that will be held before baking, hence their greater use in commercial situations. They wouldn't be as useful for recipes that depend on the initial gas release for a significant portion of bubble production during mixing.
The link quoted above also gives some specific examples of different types of chemicals used for baking powders (represented in the acronyms here):
Each possible chemical in baking powder has a particular profile in terms of how fast it reacts at various temperatures. Emphasis on early and low temperature reaction will produce a product that is denser (but still uniform in structure), while exclusively using a product that won't react until high temperatures could risk cracking and might even reduce volume because the structure of the cake begins to set before the leavening reaction is completed.
Most general-purpose baking powders aim for a balance that both enhances early bubbles in the batter and produces gases to enlarge those bubbles and add volume during baking.