I don't think a mentor has to be a drill sergeant to inspire graduate students to be productive. I definitely think a mentor can be "laid back" in demeanor and style and still have high expectations. I work at a university with a "laid back" program that still has high expectations for students. "Laid back" in this case means -- supportive, cooperative, students can dress more casually than you'd expect, mentors don't yell or get spiteful but find better ways of motivating students, etc.
I, personally, don't see myself being able to work for a person who had a drill sergeant attitude with me. I just cannot be productive with someone breathing down my neck (anxiety will make me shut down). But I am incredibly productive with a supportive atmosphere, and I'm convinced that in the right program (i.e., one with high expectations, but low stress-due-to-politics) I will get pretty far.
I think this is what the OP means.
Like the OP, I am a perfectionist and very anxious. I work for a VERY productive researcher and have achieved 11 publications in the two years I have worked for him. He is 35 and has over 190 publications (this man is insane). But at the same time, he's totally "laid back" (a bunch of us went out to karaoke and he kept buying people drinks haha, and he brings his 2 year old to work sometimes. He also curses like a sailor, and so I get to feel comfortable doing the same). Oh, and he has NEVER been harsh with me, rarely criticizes me, etc. I work hard, and he praises me, and that's mostly how we interact. If he had been a drill sergeant, I doubt I could have been so bold as to suggest the independent projects I suggested, to ask for work that would earn me authorship, etc. Working with someone who is personable in this way is the best way for an anxious person like me to succeed.