Yes, let's do think about it.
Something solid, say a stump or protruding piece of ledge, has to be high enough to contact the front of the mower deck. Depending on how you have the cutter set, that's at least 8" off the ground, more like 10 or 12. If it was shorter it would raise heck with the blades but not do what you are describing. It can't be in the tire tracks or you'd notice long before the cutter hit it. And it has to be low enough it doesn't hit your front axle, any of the undercarriage, or the drawbar. It has to be exactly the right height within pretty narrow limits, and in exactly the right place relative to the path of travel.
Assuming you actually found such an obstacle and missed it with the tires, it is going to hit the front edge of the deck. The pivot point is not your 3-point hitch pins, but the hinge point where the triangular frame that attaches to the 3-point hitch is connected to the cutter deck. The cutter in the OP's photos seems pretty normal - that's 3" or less above the top of the cutter deck. So the force being applied by the solid object has about a 3" lever arm to work with.
The center of gravity of the cutter is about where the gearbox is. It, and the rotating stuff attached to it are much of the heavy stuff, and the deck and other stuff is roughly equally distributed around it. Assuming a 60" cutter, that's at least 30" behind the hinge point. Looking at Bush Hog's lightest cutter, it weights about 500 lb.
So you have 500 lb 30" back, being raised against a 3" lever arm. That means it would take a 5,000 lb force generated by your tractor against the solid object. That's twice what the OP's tractor weighs. You think it would be able to apply that kind of force? I don't.
But assuming it could, I'm pretty sure something, like that puny triangular hitch frame, will break before the cutter is tipped up.
But assuming it didn't. how would that little flat bar help? I flat bar is hardly stronger than a chain in compression. If you had enough force to tip up the cutter that little bar wouldn't help at all.
Sorry, I don't believe there's a real issue here one way or the other.
Terry