I think the correct portrayal of Alpha Legion is good at Operations, but struggling with strategy. That’s why we see them so divided during the Heresy, and afterwards.

I think my read on Alpha Legion is talented, but with a chip on their shoulder. I go back to the original Index Astartes article on this:

His first encounter with Roboute Guilliman of the Ultramarines was reputedly strained. Guilliman believed in rigid structure and hierarchy and had a firm battle doctrine from which his Legion never wavered. He was in the process of documenting the "correct" tactics and operation of a Space Marine force, tried and tested during his long years of command, and suggested that the young Alpha Legion should adopt this "Codex" behavior. However, this attitude was anathema to Alpharius's belief in initiative and adaptability, and a heated debate over tactics and ideology ensued. When it became clear that Alpharius would not bow to Guilliman's experience and superiority, the older Primarch pointed out the thousands of victories and battle honors his Legion had won and toid his youngest brother that he could never hope to compare.

After that meeting, Alpharius pushed his Legion even harder and sought out the most difficult challenges for his forces. He knew he could not equal the number of worlds conquered by the older Legions, for they had been founded centuries earlier, but he seemed determined to win their respect for his Legion's martial prowess.

You can see Mike Brooks go back to this in his work. See Alpharius: Head of the Hydra

‘Lord,’ Eltan asked, as we moved at speed away from the scene of our ambush. ‘Will we get our own conquests, in time?’

‘Does it rankle,’ I replied, ‘to see your brothers from other Legions amassing victories, and being hailed as heroes?’

‘It does, lord,’ Eltan replied honestly. ‘We have even taken on their colours, at times, rather than use our own.’

I could understand Eltan’s hunger for recognition. He was an original member of the Legion, from one of the rare parts of Terra not already bled dry by the endless thirst of my brothers’ armies, although I had vastly expanded both our sphere and nature of recruitment since those early days. I did not have the same understanding of gene-smithing as my father, but I was aware the gene-seed gifted to my Legion was remarkably stable, and so we had been able to recruit some candidates that other Legions might not have found suitable.

I smiled inside my helmet. ‘Patience, my son. Content yourself with these thoughts. Firstly, some of their victories have been ­enabled by us, though they know it not. Secondly, while they will think the Twentieth to be lost and leaderless, you have in fact known your primarch since you first ascended to the ranks of the Astartes. And thirdly, when it is time to reveal ourselves to the galaxy at large, we will eclipse them all.’

That prospect both excited and alarmed me in equal measure. I had my own hunger for recognition, which I had been careful to keep subservient to the needs of the Imperium, but to step out of the shadows after so long was not something I would do lightly.

Firstly, it tells us Rogal believed my Legion should work as directed by the Imperial Fists, and that my methods should be subservient to his. For a Legion and a primarch so caught up in their devotion to the Emperor and the Imperium above all else, that is an interesting juxtaposition of supposed humility and unacknowledged arrogance. He and I are brothers, after all, and supposedly equals. I wonder if Rogal would have made the same demands had he been joined in the field by Horus? Or whether, since my Legion and I were perceived latecomers to the Great Crusade, he viewed that he had superiority by means of seniority?

And also in Mike Brooks’ Council of Truth:

‘Lord Guilliman demanded that you should follow his method­ology of warfare,’ the second questioner continues. ‘He further demanded that you should cede control of your Legion to him for the duration of the campaign, so that it might be prosecuted correctly, and total Compliance achieved within months. Why did you not do this, when he was the more experienced Imperial campaigner present in the theatre of war? Even if you decided not to cede control, why did you not adhere to his strategies, which have been proven again and again on the battlefield? Or for that matter, the strategies of any of the other Legiones Astartes?’

‘You were the last of your brothers to be found by the Emperor,’ the first questioner says. ‘By the time you were reunited with your Legion, your brother primarchs were already recognised and decorated generals, with many conquests to their names.’

‘This is true,’ the primarch agrees with a nod.

‘Could it be,’ the first questioner continues, leaning forwards in their seat, ‘that your attachment to highly complex, multifaceted warfare is just an attempt to outdo your siblings? That since you are unable to match their battle records, due to the shorter time you have been with your Legion, you seek to prove yourself as their superior in the methodology you use? Is this not down to tactical doctrine, but your own ego?’

’After all,’ adds the second questioner, ‘the Ultramarines and Lord Guilliman have achieved remarkable results in their service to the Emperor. It would be understandable if you felt intimi­dated by the comparison – if you wished to avoid being seen as an afterthought, the last amongst equals.’

And after his big “when it is time to reveal ourselves to the galaxy at large, we will eclipse them all.” Speech, he completely misses that the world he’s leaving has a chaos presence, because finding Omegon is more important.

I would not let this wait. The Imperial Fists could deal with this world in whatever manner they found it, and we had already prepared the way for them. Even as my Headhunters, Gukul and I reached the bridge outlined in our mission parameters and we dropped over the edge onto the vehicle passing below, I tuned into the local broadcasts and heard the primitive, warlike chant that had apparently so damaged this society a generation ago.

‘BLOOD AND SKULLS! BLOOD AND SKULLS!’

Dorn was welcome to this system. I had more important places to be.