Claremont explored her journey into leadership in depth in the original run. To begin with, Storm was merely one of the team, and Cyclops was field commander and Xavier the founder and overall leader. Now, she did prove to be hugely instrumental to her first three missions(powering up Polaris for the field reversal, and sweeping the soldiers away from the halls of that military base without hurting them, and taking out the cairn from that demon Cyclops unleashed when crying in the woods about Thunderbird), establishing right from the start she was the powerhouse(before Jean even starting her development as Phoenix). But she was also very naive about modern, Western culture, having lived in tune with nature as a goddess since her tweens. Despite being a little insecure in that regard, she definitely had no problem speaking her mind even early on, so the force of will necessary for leadership was always there.
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It is not until after the DPS, when Jean sacrifices herself and Cyclops leaves the team that the mantle of leadership is thrust upon her. She didn't want it, necessarily, but Xavier chose her, and she rose to the occasion. The other team members, including Logan who is of course much older than her and even more experienced in terms of military operations and so forth, do defer to her lead, even in ways surpassing what they would Scott, because she had earned their respect through the many adventures they had already been on together. Days of Future Past was Storm's first big mission as leader, and I really love seeing all her thoughts as the story unfolds, especially in contrast to the older, hardened Ororo in the future timeline(I'm really bummed the movie version took all this away from Storm onscreen).
Storm begins to hit her stride through the early 80's, especially when she has to contend with Scott coming back into the fold, during which she does have the opportunity to see what it is like to not lead for a time, and to realize, while he might be more experienced than her, that she does have her own talents she brings to the table. Experience vs skill, as it was distilled in that Danger Room session they were playing. Between that and Xavier reasserting himself when he gets his new clone body(and Ororo having just gone through her own tribulations in the Brood saga), she really had to decide to abandon the Ororo windrider she was, goddess of life, and embrace being Storm, who must battle and potentially kill to serve her team and mission statement. This is of course exemplified in her duel against Callisto, where she stabbed her in the heart(something she knew Kurt could not do) to save Angel and get her team out of there before they were overwhelmed by the Morlocks. Callisto would have died had the Healer not done his work. Ororo had broken her vow never to kill (again, just after the whole Brood abortion/suicide). Ororo windrider was over. Storm had won.
Of course from there we see Storm continue her development as a leader, first when dealing with Rogue's acceptance by Xavier, and then Yukio's influence in Tokoyo. That Mastermind fight see's her starting to embrace a darker aspect of herself with the brutal use of her powers. Of course she then looses her powers not long after that, thanks to Forge's depowering gun, and that begins an even greater developmental arc, where she first realizes she is more than her powers and still leads the team without her powers, leaning into her tactics and team strategies. This is underscored in her duel with Scott. While Inferno did later retcon Maddie as psionically distracting Scott so he would loose, the fact is that Ororo did find a way to neutralize his attacks and show that his [uncontrolled]power was more of a liability than her lack of power.
Her sentiments changed soon after, though, when the Mutant Massacre hit. Without her powers, she wasn't as effective on the field. And her team and Morlocks suffered. She had a break down. It was all too much(and at the time the story was rather revolutionary for the medium and Marvel in particular). Callisto helped her find her nerve again, and that's when she started to really get dangerous. That issue where she fights the three old supes, Crimson Commando, Stonewall, and the Whizzer(?), she went full Batman. Even after developing to that level, though, she realized she needed her powers back to be at her best. That leads to the whole Fall of the Mutants arc and then the fateful decision to 'stay dead' with Roma's resurrection of the team after their sacrifice at Forge's hand to stop the Adversary.
Outback era Storm was Rightclops 30 years before Rightclops. Storm had the sneakiness and ferocity of her depowered period, plus her powers at full potential, with a strike team that could teleport in and out anywhere around the world. The Outback era melts into the disassembled era, and eventually wraps up the Claremont run with the summation of the Genosha situation, the Shadow King/Legion saga, and the reintegration of the X-Men and X-Factor to create the Blue/Gold strike forces. By that time Storm and Cyclops are regarded as complete equals, and both the equal/or at least approaching the level of Captain America himself in terms of leadership.
I can remember a scene of Storm, Cable, Cyclops and Jean in the mansion's war room just before X-Men/X-Force #1, and they are plotting out all their loose ends and Storm is really pushing for a proactive stance that entices Cable, but surprises Scott and Jean. They(Scott and Ororo) both essentially share leadership throughout the entire decade, and even into the early 2000's, where Ororo breaks off from the mansion for X-Treme and Scott becomes less central as part of the faculty(with Xavier as headmaster, and eventually Jean taking that role too). That was some of the best times for Storm as a leader, and Claremont really showed how it was basically integral to her being. That's just how she rolls. She has the fortitude, the ability, the vision, and the willpower and determination to see it through, not to mention the goodwill of her teammates and the respect of key figures in the wider superhero/political world. At least Claremont's Ororo does.
Obviously not so much with these other 'writers'.....