It seems to me that the aim should be to have battens that are strong enough to allow the boat to be driven hard, and to survive squalls, no matter what type of hull you have. Once you have achieved this, then it is just a matter of reducing sail area, whether on or off the wind, to keep control of the vessel, and this will indeed depend on hull type.
They all have their advantages. I've surfed downwind for long periods in light-displacement boats, which was huge fun. They were easy to steer, but required constant attention to the helm. Displacement hulls obviously won't surf, and if you drive them too hard, are liable to broach, whereupon you may well start breaking things.
The displacement hull is easier set up for self-steering in my opinion, but there are always exceptions to the rule. People do use autopilots successfully when surfing downwind on light boats, but if the autopilot fails on the face of a large wave, chaos may ensue. A few of the round-the-world racing yachts have capsized when their autopilots broke while surfing. I would not choose a light-displacement flyer for solo ocean cruising, but others have. John Guzzwell's Trekka was light, and he surfed at times. More recently, Webb Chiles circumnavigated solo in his light-displacement Moore 24, Gannet, regularly replacing autopilots along the way, and says it is the best offshore yacht he has ever owned.
I drove my 24' (7.3m), 5-ton, junk sloop, Arion, very hard downwind. We were never likely to surf, but surged on the crests of waves for long periods at times. That boat never showed any sign of broaching, even under its previous bermudan rig. With the junk rig, I eased the sheet right out until the upper sheeted batten was athwartships, and the unsheeted batten above it, plus the yard, were beyond athwartships.
How you sail your boat will depend on many factors, including design and personal preferences, but the yard and battens should be stout enough not to break except under exceptional circumstances. It should not be determined by the amount of sail you carry. The only consideration for reducing sail should be the control of the vessel. It will also depend on the sort of cruising you do. For inshore or coastal cruising, I'm quite happy to drive the boat hard, but for offshore passages I subscribe to Roger Taylor's philosophy of easing along.