Generally not in the U.S., unless it's a civil or electrical engineer designing infrastructure. I say this as an aerospace engineer with a mathematics PhD only.
I once interviewed a CS grad from MIT for a mid-level software engineering position; smart guy. Couldn't code. Sorry sir, but we need someone that can contribute immediately. We don't care about your school. We care about your output. Next.
(2) Even if they can't pass those questions doesn't mean they can't code.
45 minutes with someone gives you an idea of what they can do, a decent sample. However, graduation from a university signals that they have been sampled repeatedly for years. They can clearly learn, and should (assuming the system is semi-efficiant) and can do what the university accredited them for.
Even if they screw up that one interview, it means little by itself (baring massive failures during the interview).
That's not the whole issue. If you remove the loan payback guarantee, then creditors will start to evaluate the creditworthiness of students and their families when deciding whether to offer educational loans. Poor families not being able to get loans is a political no-go.
Universities accredit them, so companies don't have to spend their money doing it (via a ridiculous number of interviews). Interviewing is already one of the largest sinks of money for a largish company, no need to make it worse.
Far better, would removing the guaranteed loan payback the government provides. This would force universities to lower prices as students wouldn't be eligible for loans. Further, it increases the barrier to universities, meaning less people will have degrees and in turn companies would have an incentive to hire people without degrees. Plus people with degrees would get paid more (making it easier to pay off loans).
The whole issue is universities aren't having to deal with market forces. Add back in the incentives and it'll be 10x cheaper.