Nobles can be adventurers, running things only takes so many hours a week. Besides that, noble pledge packages come with several sparks and souls allowing for the creation of a second character for adventuring.

I mean no matter what you pledge, you'd have to come & check on your personal territory every 30 days to not lose it regardless. So, to a degree, adventuring is limited for everyone, unless you're willing to forsake all & live on the open road simply by luck. I plan to pledge proprietor, and I'm not exactly sure what all that entails, but hopefully I'm not too bound to the town. I wanted to pledge high enough to make my mark & get into the exposition, but not be bound by too many limitations. I don't think the gentry level pledges are as restricted as the aristocrats. I could be very wrong though. You just might know more than me. XD

Any action has its risks, and adventuring as a noble is surely risky. But if you take in consideration the greater access to resources a noble might have, those resources might outweigh the risks. Better armor, better maps, a security force, etc. Adventuring as a noble is not impossible. In fact, the game is more likely to reward nobles who adventure through Story Points. Disguises offer some cover for nobles who wish to explore and adventure but who do not wish to let it be known they are gone.

Well high level nobility will have whole set of their own adventures to experience, for example as Duke I intend to know every part of my Duchy intimately, first I will explore my own county, map it, then go explore county of my duchess, then rest of my counts, it will take time to do , in between my responsibilities of running it, but to run something I need to know first hand what I have , so there will be adventuring for everyone , nothing is stopping you to write your own story