No direct reports. There are multiple Principals in the same situation. No direct reports, they just usually work on a scope that involves multiple teams,but they don't lead them.
As a Principal I do code less than I used to as Staff or Senior. But I still do a fair amount of coding (along with design, arch, mentoring/guiding). I've made it clear that I want to remain a hands on engineer, and my company has let me remain so.
Not everyone is so lucky to have a choice, but if you do -- In the end, its finding a place where you can get the balance that makes you happy.
When management track people have direct reports it's usually like here's six people to manage. Three of them are junior-level and need constant hand-holding.