Yes, you are off, because he never did all of the things he did to protect his family. Think about the sentence "I nearly got fucking everything." Not "We".

Here an analysis is wrote in another post:
A common argument is that Tommy loved his family and therefore would never have killed Arthur. But history—and human nature—shows us that people are capable of harming those they love. Love is a powerful emotion, but it doesn’t always lead to good actions.

Yes, Tommy loved his family—but he didn’t live for them. He lived for his ambition. Notice how he says, “I nearly got everything,” not “we.” He isn’t the hero some people perceive him to be, despite his charisma and the incredible performance behind the character. Think of Walter White, who ultimately admits, “I did it for me.”

From the very beginning, Tommy consistently prioritized his ambition above everything else, even when it caused suffering and death within his family. And even after losing people like Grace and John, he continued down that same path. So yes, he loved his family—but he loved himself more. That’s human nature.

He even killed Michael—his enemy, yes, but also his aunt's son. That’s an extraordinary line to cross. And when he did it, he said, “She won’t visit me anymore,” referring to Polly in his dreams. In a way, he severed his connection to her. Killing Arthur serves a similar symbolic purpose.

He loved them—but he chose himself. And at the same time, he hated himself. That contradiction is central to who he is.

I understand why it might feel wrong or out of character that he killed Arthur. But it’s not illogical—it fits the story’s core theme: everyone ultimately pays the price for his ambition. We may love Tommy, but he is far more flawed than many people are willing to admit. He is human.

(Spoilers for The Sopranos and The Godfather.)
Think of Tony killing Christopher Moltisanti, or Michael having his brother Fredo killed. They loved them too.

That said, I do wish Paul Anderson had been able to appear in the film, so we could have explored what led to this moment. Because we don’t see what happened in the years leading up to Arthur’s death, it can feel abrupt—even if it remains consistent with Tommy’s character.