I think that #2 plays that way because it is generous off the and hard to get up and down. The bad player is not going to lose strokes to lost balls, out of bounds, or water. Therefore, their inconsistent long game doesn't get penalized as much as at other courses. The good player generally doesn't worry about that at any course. The good player shoots good scores because of their generally better short games. But, at #2 it is generally very difficult to get up and down unless you miss it in the right spot every hole. And on each hole that changes depending on the pin position. However, the bad player generally doesn't get up and down that much. They often take two chips or chip on and two putt regardless of the course. So, #2's difficult greens don't affect them as much as the good player.
The good player must have an intimate knowledge of the course and its strategy to shoot a good score at #2. There are some places you will almost never get up and down from and some you can quite easily but you wouldn't think it at first glance.
As an example, on the first hole the players generally will miss right because they don't want to be in the bunker. That is a very difficult up and down because the green rises a foot or two from that fairway area and the green runs away from you. The good player makes a lot of fives from there on what is one of the easier holes on the course. But, the bad player isn't going to get up and down much anyway. So, they run it or putt it on the green to 20 feet and two putt for their 5. Both players end up with the same score. The good one knows he screwed up with a very difficult second hole coming and the bad player is happy with the five. However, the good player needs to know that it is far easier to get up and down from the bunker, even though it appears deep, because the green is sloping towards you. That makes the bunker shot much easier to control. The slope of that green from back right to front left is also why you need to the bunkers on the left off the tee. It is much easier to hit the green from there than the apparently safe tee shot down the right that doesn't require you to carry the bunker on the second. But, you are always hitting something less than 8 iron anyway.
I could go on like this for every hole at #2. There is an ton of strategy that is not apparent at first glance. And, that strategy is much more in play after the renovation.