One element of physics favors an immediate response, all else equal: the draft behind a cyclist declines very rapidly with distance. If you want to catch on to an attack, an immediate response is optimal. If you delay until someone is a hundred meters up the road, you now have to expend much more energy to catch them. That explains why in the general case of a breakaway, people who want to try to get into that breakaway should respond as early as possible. That said, the breakaway might not last, and there might be another selective terrain feature closer to the finish that could favor a breakaway.

If we're talking about the general classification (GC) race, that is for overall victory, there are a number of reasons a GC contender could have decided to respond immediately to an attack. The motivation might be psychological - they might want to show that they're on par with or close to the attacker. The draft is still at play, even on climbs. Bonus seconds for the top three placings might be at play, although they weren't in stage 2. You might also want to put time on the other contenders. And there's uncertainty at play, because you don't know how much time the other rider may take. Hence, you might want to stay close.

In other GC contexts, you're right that you might not want to respond immediately to an attack by someone else contending for GC. You might be able to handle variable power more poorly than the other rider. If you are at your limit, going further above your threshold will be costly. You might accept some time loss if you know you can make it up in the time trial, and Vingegaard is thought to be better at TTs than Pogačar. Or you might be able to figure that the other rider is riding over their limit and they could crack - I don't know how often that happens these days, but this could be more of an issue before power-based training.

Vingegaard in 2024 is also a special case, because his preparation is impaired due to an earlier injury. He might be thinking that the effort would help him race into shape - he would be fresher than others, in some ways, so that might be an acceptable risk. Or it's also a gauge of form. Indeed, the media are taking his performance as a positive sign.

One element of physics favors an immediate response, all else equal: the draft behind a cyclist declines very rapidly with distance. If you want to catch on to an attack, an immediate response is optimal. If you delay until someone is a hundred meters up the road, you now have to expend much more energy to catch them. That explains why in the general case of a breakaway, people who want to try to get into that breakaway should respond as early as possible. That said, the breakaway might not last, and there might be another selective terrain feature closer to the finish that could favor a breakaway.

General classification factors in responding

Let's talk about the general classification (GC) race, that is for overall victory. At the top level, the physiological gaps between top athletes are very small. When you see gaps of multiple minutes in the grand tours, those are the product of differences over many days - 21 for the men.

Psychology is one factor. Absolutely no amount of positive psychology could even let me finish the Tour in the grupetto, but it is still at play in the GC. Kit Nicholson of the Escape Collective argued that Pogačar's attack on stage 9 (the stage with gravel sectors) was in part to try to land a psychological blow. An immediate response might similarly be motivated by wanting to show that you're close or equal to the attacker. 

The draft is still at play, even on climbs. Bonus seconds for the top three placings might be at play, although they weren't in stage 2. You might also want to put time on the other contenders. And there's uncertainty at play, because you don't know how much time the other rider may take. Hence, you might want to stay close.

In other GC contexts, you're right that you might not want to respond immediately to an attack by someone else contending for GC. You might be able to handle variable power more poorly than the other rider. If you are at your limit, going further above your threshold will be costly. You might accept some time loss if you know you can make it up in the time trial, and Vingegaard is thought to be better at TTs than Pogačar. Or you might be able to figure that the other rider is riding over their limit and they could crack - I don't know how often that happens these days, but this could be more of an issue before power-based training.

Vingegaard in 2024 is also a special case, because his preparation is impaired due to an earlier injury. He might be thinking that the effort would help him race into shape - he would be fresher than others, in some ways, so that might be an acceptable risk. Or it's also a gauge of form. Indeed, the media are taking his performance as a positive sign.