See, here's the thing, that's not how the show describes what being a true alpha is. It does not say that a true alpha is 'pure of heart', or 'such a good person'.
In the show being a true alpha is described as such, it's something you become "Through virtue, strength of character, and force of will".
Now virtue does not mean 'being pure of heart', it means standing up for what you believe in, all of it is connected through will power, through standing up for what you believe in, not because someone pushes you to do so , but because of your own beliefs. And to have the strength of character and force of will to back that up.
And there's not much twee about that.
Peter tried to make it sound that way. When he attacks Scott in the s4 finale, but remember, Peter is a very unreliable narrator in any and all circumstances.
The mistake fandom makes is to assume that being a true alpha is some way to give an alpha extra powers, when really it's just a way to become an alpha. (I personally headcanon, that it's the original way alphas first came to be, but with time, the alpha power was transferred through inheritance with the death of the previous alpha, or through theft, as the new alpha killed the previous one. And there were fewer and fewer 'true alphas', because there was less of a need for them)
Derek's issue in s2 is that he was never trained to be an alpha, and the alphas he had before, were his mother and his older sister. Both of whom in his eyes had a role of authority in his life. So he ignores the familial role he was supposed to have as an alpha, and tried to grasp for authority instead, which only ended up turning his betas against him. Because a pack is not supposed to be a military unit, it' supposed to be a family.
Scott on the other hand is very much a strategist, something none of the other members of the pack are capable of. But as part of Scott's strategy, he knows to allow the others to do things their own way. Scott just has enough understanding of other people's personality to know what they need to be their best.
It's why Stiles would never work as a part of Derek's pack, because Derek would try to give him orders, and Stiles won't even take orders from his own father, he'd be so busy rebelling against whatever Derek tried to order him to do, that his entire potential and skills would be lost.
Scott does understand this, which is why he does not order Stiles to do anything, he may offer him suggestions when asked, but he gets that ordering Stiles around would not work. He offers kindness to Isaac, encouragement to Malia, support to Lydia, independence to Allison... and these are all things that work best for each of them individually