David, Jim,
when you see what they do with strobes in the rafters at indoor horse shows, you begin to understand where dog Agility may have to go to get decent shots. Although putting some photo floods out might work too. I'm just not into climbing up into the beams and ceilings of most of those venues.
Just because it's always been done without strobes doesn't mean you can't change it. I think the issue is on-camera strobes rather than stuff placed high to illuminate the entire space. Same goes for sporting events such as hockey and basketball so it's been done. And those events have comparatively wonderful lighting!
Jim