I thought that solar panels mounted on the north slope of a roof would be useless, but I was wrong. Our home is oriented east-west, with a southern and northern roof exposure and a 15 degree slope. Our solar system includes a monitor which reports the daily production from each of our 29 panels. The panels on the northern slope make a significant contribution, producing about 2/3 to 1/2 of the kWh the panels on the southern slope do, depending on the season. The solar contractor had access to some type of satellite data which told him exactly how much sunlight our roof received, and his estimate of what the system would produce month by month was amazingly accurate, if a little understated.
The panels we have are both light and tough. The workers carried them to the roof two at a time over their shoulder with one arm, using the other arm to cling to the ladder, and we have been through two hailstorms without damage, including one storm which dropped marble sized ice balls and which mowed down he 4ft corn stalks in our garden.
Yes there are a number of ways to maximize potential but it still boils down to the problem of BEING IN THE WAY and dealing with the lifetime problems of roof replacement and maintenance, not to mention about how your home insurer or your HOA feels about them.
Still, IMO, the best place for them is not on the roof, period.