What examples are there of jobs which can make use of high general intelligence, that at the same time don't require rare domain-specific skills?

A manager :-) A business manager, a small business owner, a civil servant, a dictator, a leader of the free world :-/

Generally speaking, there is something of a Catch-22 situation. The low-level entry jobs are easy to get into, but they don't really care about your intelligence. But high-level jobs where intelligence matters require demonstration not only of intelligence, but also of the ability to use it which basically means they want to see past achievements and accomplishments.

There are shortcuts, but they are usually called "graduate schools".