Sponge cake - Why mix milk and butter instead of folding?

I can't say why you'd want to do this in general for other types of sponge cakes. But in the linked recipe it's very clear. The reason is because the milk/butter mixture is heated "to just under a boil" and according to the instructions should still be at least "hot (about 150F)" when added.

In this case, you take out a small portion of the batter, then add this hot liquid mixture to it. If you don't mix rapidly while doing so and if the temperature is a little off and too hot, you run the risk of coagulating the eggs in the batter (which would obviously not result in a desirable texture to add back into the rest of the batter).

Here, as the recipe notes, you're using this portion of the batter as a liaison, which is a fancy word for a mixture the serves as an intermediary temperature between something hot and something cooler. By adding the hot milk/butter mixture to a small portion of the batter (rather than the whole batter), you cool it enough so that it won't risk coagulating eggs in the whole batter.

But in the process, you need to whisk rapidly to avoid small egg bits forming curds and becoming solid, so you're sacrificing some of the bubbles in this portion of the batter to create an appropriate intermediary temperature mixture, which then is presumably supposed to be gently folded back into the rest of the batter.

Now, the question is why you're heating the milk in the first place. There is a whole genre of cakes called "hot milk cakes" or "hot milk sponge cakes," which seem to have originated in the early 20th century. They use this rather unusual mixing method, where you beat the sugar and eggs for a long time first, then add flour and dry ingredients, and then add liquid and fat at the end.

I'd speculate that the hot milk serves two purposes: (1) it helps melt the butter, which both allows the liquid butter to combine easier with the existing mixture and causes it to coat the flour better which results in a tender crumb (less gluten network formation), and (2) it raises the temperature of the batter above room temperature, thus shortening the time before the cake structure starts to solidify while baking. My guess is that this is helpful because the sugar/egg foam is less stable than, say, a sugar/butter "creamed" foam (as in a pound cake), and if you don't get the eggs to coagulate fast enough, the whole thing might collapse. (Again, that last part is just a guess.) The goal is to end up with a very light and tender cake.