Yeah my Promaster City originally had 5.2" clearance, same as a Prius. Went through 2 oil pans, but that's mostly from tackling trails like the third example. Now with my lift and AT tires, I have about 7".
Mainly I wanted the AT tires 'cause I've gone through a lot of irreparable flats (mostly sidewalk punctures.) But the clearance will help. Especially if I keep going places I shouldn't. Which I likely will.
RE: What Are BLM and Forest Service Roads Like to Drive?