To expand upon Jiro's points:

Irvine explains in Trabia during the basketball scene "I thought you guys all knew" he freaked out not only because as a sniper his name goes down in history as the one who shot Edea something like that is not a small task, think about if JFK had been a sanctioned assassination of the CIA/Secret Service. Think about if that agent taking the shot had truly been named as the assassin? How would he cope with the pressure of something so monumentally big? Remember he doesn't have to hate JFK or be doing it because he agrees with the need of it being done, he's just a following an order from above. But he freaked out because above all Edea was Matron and Matron was essentially like a mother to him during his formative years and he loved her. And there she is with Seifer who he may or may not recognize but certainly would remember the name of someone he knows he will have to kill right afterwards. He's conflicted on two fronts, he never asked for the mission, he didn't necessarily want the mission and now he's about to perform the biggest assassination in living memory and making matters harder it's the woman who raised him as a child and down there with her is one of his childhood friends.

In the Balamb Garden civil-war situation. Which btw was over way too quickly though I get the need for urgency considering at the same time Trabia had just been blown to smurf and Selphie's team were on a suicide mission to stop the missiles being launched for Balamb but it feels like this could have been explored more. Perhaps some battles against SeeD supporters of NORG, with Squall and company leaving them wounded but not deceased. Or even a side quest during the 3 days of drifting at sea before hitting FH to heal the rifts (as the only squad not involved they'd make the ideal peace keeping force). When the squad eventually confronts NORG he says that the order for Edea's assassination had come from him but it was not meant to be given to Squall, Martine was supposed to carry out the mission with forces from Gabaldia Garden (so Irvine still would have been involved I suppose) however Martine used the opportunity of Squall's arrival at the Garden to pass blame over to Balamb Garden. NORG attacks the squad with the intent of killing them because he needs to appease the Sorceress Edea by handing over the heads of the SeeDs involved on a platter. Squall and co basically aren't going to take this laying down and so kill the old Shumi bastard before he can kill them.

Laguna, Kiros and Ward's story would have made a good game tbh yes, certainly I feel the 3 characters weren't as developed as they could have been. Laguna and Julia as a love story was never going to happen. Julia invited Laguna to her room, they talk and Laguna falls asleep drinking wine. Julia is pouring out her heart to the man and he fell asleep. When Kiros arrives in Winhill he mentions Julia married General Caraway and that they say she was in love with a soldier who went to war and never came back home and that is who she wrote Eyes On Me about. We know that it is Laguna as the players but Laguna doesn't even seem to acknowledge it was him even though Kiros is saying it with a knowing "hey dude I'm talking about you" style. Laguna then fell in love with Raine and married her, yet when Ellone was kidnapped by the Estharian forces from Winhill he went chasing off with Kiros and recruited Ward along the way on a rescue mission that took so long he never saw Raine again, she gave birth to their son and died without ever seeing the man she loved again. Where was Laguna at this time? Well for some of it he was starring in a low budget movie adaptation of "The Sorceresses' Knight" which ironically is a movie of Seifer's favourite book to earn more money to try and find Ellone. He then makes it to Esthar where he winds up as a member of the resistance against Adel and manages to trick her in to meeting him at Tears Point and then manages to surprise her long enough for the resistance to freeze her. He is elected president of Esthar but he seemingly doesn't send for Raine. Bear in mind that Adel is frozen precisely 17 years prior to the events of FFVIII taking place. Squall is precisely 17 years old at the time of FFVIII so Laguna technically could have had time to send for Raine or to find out that she died in childbirth and he has a son who lives in an orphanage for war children he could have taken some responsibility as a father.

That being said the 3rd disc seems too short, after the Lunar Cry was a perfect opportunity for them to introduce the first "Mark" quest type or perhaps at least an optional side missions to make the 3rd disc grind more appealing in the form of "This is Esthar command, we need support from SeeD on X Y and Z locations, can Garden respond?" This would have led to interesting situations where the player could have split the squad a-la missile base or even introduced additional "party guest members" to round numbers out, perhaps giving characters like Xu or Nida a chance to shine and actually help the squad in battle.

Overall FFVIII is far from a bad game or even the worst in the FF series. However it did miss out on plenty of additional content or perhaps story what could have been in-put without ruining the core of the game. It also did a poor job of explaining motives/events/characters at times but then so did FFVII a game which is often regarded as the best in the series.