but they would have to spend an equal amount of time over the southern hemisphere
There are some highly eccentric orbits which are heavily tilted so that, time-wise, they spend more time in one hemisphere than the other, by tracking farther away from the earth when slowly overlooking the northern hemisphere, and then getting closer to the earth when tracking the southern hemisphere, faster. The Molniya orbit is one example. There is a diagram showing how much time the orbit spends in each hemisphere.
For use in telecommunications, the fact that the satellite gets farther away is usually acceptable, although this wouldn’t be as good for a spy satellite.
There are some highly eccentric orbits which are heavily tilted so that, time-wise, they spend more time in one hemisphere than the other, by tracking farther away from the earth when slowly overlooking the northern hemisphere, and then getting closer to the earth when tracking the southern hemisphere, faster. The Molniya orbit is one example. There is a diagram showing how much time the orbit spends in each hemisphere.
For use in telecommunications, the fact that the satellite gets farther away is usually acceptable, although this wouldn’t be as good for a spy satellite.