Indications that Tom Hagen wasn't a war-time consigliere

Sonny, in an outburst, tells Tom, "You're not a wartime consigliere." Later, Tom asks Michael, "Why am I out?" Michael responds, "You're not a wartime consigliere." Vito also mentions that he advised Michael. Therefore, Vito presumably didn't think think Tom is a wartime consigliere too

What were some signs that Tom wasn't a wartime consigliere? So far, I think these are signs:

1). After Vito is shot, Tom's advice leans towards negotiating and making deals with Sollozo / Tattalgia. Tom also pushes the "Don't take this personal" remark on Sonny, which Michael strikes down by noting that "they want Pop dead. That's it." Tom's propensity towards making a deal indicates that Tom doesn't like fighting and killing. He would've never given advice to shoot Sollozo and McClusky.

2). When Sonny dies, Tom doesn't immediately tell Vito. Tom instead sits in a room to have a drink; Vito himself has to go limping towards Tom and gently drag the news out ("but first you needed a drink?"). Later, Tom, much to the annoyance of Michael, hestitates to deliver to news to Michael about the miscarriage. Tom's behavior in these scenes shows that he just doesn't have the stomach for dealing with morbid events, the way a wartime consigliere would

3). When conferring with Michael in Part 2 about the Senate Hearings and Hymen Roth - Michael suggests a meeting with Fredo to find out what Fredo knows. Hagen tells Michael, "I don't think he [Fredo] knows much." Regardless, Michael says, "I want to meet Fredo." During their meeting, Fredo reveals that one of the Senators investigating Michael is on Roth's payroll. Thus, Hagen was wrong to suggest that Fredo didn't know anything ... Very likely, Hagen was quick to say that Fredo doesn't know anything because Hagen, aware of Fredo's betrayal, wanted to avoid a heated meeting between the brothers: he didn't want Michael to do or say something hurtful to Fredo in a meeting. Hence, Hagen again hints at an aversion of conflicts and fighting

4). In the same scene where Hagen suggests that Fredo doesn't know anything, Hagen also tells Michael, "Roth ... he played this one beautifully." Then, Michael glares at Tom with silent fury, and Tom's reaction basically says, "Sorry." This exchange can be another example of why Tom isn't a wartime consigliere. Praising and admiring Roth comes off as tactless, as Roth tried to murder Michael and his family. Hagen thus failed to read the room; he didn't realize that a Don wouldn't want to hear those sentiments about a wartime enemy. Tom's mere ability to even praise Roth also hints that Hagen doesn't fully grasp the stakes or the goal: his sole ambition should be to destroy Roth

5). During Vito's funeral, Tessio comes to Michael about the meeting, which reveals that Tessio is the traitor. Hagen is surprised; he thought Clemenza would be the traitor. But Michael knew that a deal with Barzini was the smart move and that Tessio was always the smart one. Hagen's misjudgment about Tessio/Clemenza further hints that he's not a war-time consigliere: he didn't have the ability to guage other individual's motivations and temperments

6). The instances where Hagen does best are also revealing. He is quick to tell McClusky that their bodyguards are privately hired / licensed and that McClusky would have to appear in court next morning if he blocks them. He is sharp during the Senate hearings, telling the Senator that Frankie's brother doesn't speak English, is under no subpoena, and came there on his own expense to Frankie. With Vito in Part 1, he also seems to be more of a calendar clerk. With Woltz, Hagen doesn't have to do much except look, sound, and act like a big-shot lawyer. The conclusion is that Hagen's built more for legal and administrative work, not the mafia. He belongs in the family's legitimate field.