Speaking as someone who's got a bit of experience riding singlespeeds offroad (gratuitous bike pics to follow):
I couldn't imagine riding singlespeed XC without proper foot retention. If you're just hitting the dirt jump course or the skills park then by all means ride flats, but there's NO WAY I'd make it up some of the ravine climbs in my area if I couldn't pull up on one pedal as hard I was was pushing down with the other.
PS. I used Power Grips "back in the day" when I first started riding offroad. They worked pretty well and I think I'd be more confident with those than toe clips/straps if I absolutely wasn't willing to ride clipless.