Slash has always been one of the most popular fic writing genres and the pairings you mentioned have some of the strongest and most interesting dynamics in the comics.
Cap and Tony have a long established friendship in the comics with a lot of drama added to it due to their differences and disagreements. But despite that they are also characters that tend to gravitate towards each other and usually they both suffer when they are in bad terms and tend to get emotional about it. Tony's reaction to Cap's death for example was pretty fucking strong and both Casualties of War and the Confession are some of the issues people remember most about the Civil War event.
Superman and Batman have a pretty strong relationship to the point Bruce sees Clark like the brother he never had. He also sees Clark as a shining beacon of hope which can be good but also bad since Bruce has a lot of expectations from him and in the stories when Clark doesn't meet those expectations he tends to not take it well. He also gets frustrated with him because Clark is a person that is too trusting of others and someone that will open his heart to you unless you give a reason not too. Because of this Bruce tends to be protective of him. Clark on his part thinks Bruce is a brilliant person and puts up with his eccentricities and seems to look past his Batman persona. Also the way they reacted to each other's deaths and the support they give each other when the other suffers a loss says a lot about how much they care about each other.
They also have shared many comics together with World's Finest and Superman/Batman which tend to focus on their relationship and out of the JL they have the strongest friendship.