I know plenty of capital E Engineers. None of them have whiteboard interviews. They are expected to solve problems, but none of them are expected to draw schematics for a bridge while someone watches over their shoulders.
No other non-performance based industry has this kind of weird hazing ritual. Whiteboard interviews are nothing more than the current fad--they definitely aren't necessary requirements to hire "good engineers".
2. This part is more important. School is about a lot more than exams. Projects were usually about 50% of the grade in CS classes.
If you made it through 4 years of the CS program I went through, you know how to program, or you paid someone to go for you for all 4 years.
So yeah I'd take a B average from my school as proof that you know how to program.
But I wouldn't make it a requirement.
What they need is someone who is good at solving problems, which ties into your comment about dealing with bad situations. This is something startups eventually adopt once they mature past needing a web developer to just throw together a website for them, and on to someone who is more flexible and loyal.
So please don't reduce the importance of good engineering down to "puzzles". They are a good indicator of someone who has all those qualities you describe.
And i wouldn't limit anyone to the big 5. If you believe Google's interview is pure memorisation and no problem solving, don't interview with them. My point is a good interview knows the importance of problem solving, whether solved correctly or not, is about how you solve the problem, and so they design their interviews thusly. That's my point which is contrary to the common sentiment here that "puzzle" interviews are a waste of time..
This is especially true when really wealthy companies will teach you the technologies you need to learn. You simply can't teach a good problem solving skillset, though.