I think it's more simpler that that: the pipe is the melon patch that Kaji takes care of, Kaji is nice and fatherly to Shinji, so this pipe is a nice place.
In 2.0 we see it blackened by the N² mine: the nice place is threatened (we could also extrapolate to the rest of Tokyo-3), in 3.0 it's completely twisted, rusted and in a sterile ground: the nice place (and Tokyo-3 as a whole) is dead and empty, time to move on.
Also I would like that you answer that question:
What do you means here, I'm genuinely interested?
I think it's more important than being a nice comfortable place. The aquatic zoo that the cast visits is a nice place. The melon patch is a place of learning, where Kaji teaches Shinji about responsibility.
In 2.0 it's blackened, yet about the same time the scene snaps to the pipe, we are shown Shinji's extensive struggles to reclaim his responsibility - piloting the Eva. It's not shown because a place "isn't nice" anymore; that's way too vague to even be relevant. Even if it were to represent a comfortable spot, Shinji is literally being tossed around by the explosions of an Angel. That's basically out of the question. What is the underlying message in the scene is that Shinji is picking up his responsibility.
It's the same as the watermelon patch scene. This scene was a genuine intimate moment between Shinji and Kaji. Kaji opened up to Shinji and almost thrust the responsibility of Misato onto Shinji. The underlying theme here was the same: in terms of ego states, Shinji was a child for almost the entirety of the scene, up until Kaji told him to take care of Misato. Here, Kaji exchanges roles, taking one of a child, while speaking up to Shinji as a parent figure to protect Misato. It's simple transactional analysis. The scene is about responsibility.
Again, 3.0 is the same way. 3.0 is about repeating. We've seen this shit happen again and again and we're getting tired of it, Shinji. We're getting tired of you hopping into an Eva like an obedient dog. We're tired of you teetering the Earth on your fingertip of apocalypse. We're getting tired of your stubbornness, your misguided responsibility.
The topic of responsibility is easily explained. NGE Shinji expressed serious attachment issues with various members of his intimate circle of people who knew. At a young age, Shinji(NGE/NTE) was abandoned by his father. This undoubtedly fucked with his mentality. In 2, Shinji directly states that he does not know what it be a grown up. A lot of Shinji's inner struggles are ones of responsibility. Yet one responsibility he has accepted, if only to please his father, is piloting a giant robot. This is Shinji's responsibility under NERV's command.
So the pipe, representing responsibility, is shown, again. This time, it's all old and bent out. And, likewise, is Shinji's responsibility to piloting an Eva. In Q, he's aggressively swept into an Eva. However, he keeps piloting it out of his own responsibility - this time, he wants things to go back to normal, and naturally this thought is accompanied by an immense guilty feeling. We, the viewers, know he's impulsive and is rushing into bad news again. But the pipe still stands out in the scene because Shinji still holds a valid grip on his identity with an Evangelion robot - it's his responsibility to pilot it, even if he shouldn't be.