Here's the thread California was talking about:
Broken lift housing.
I can easily see how a backhoe on the back would break a tractor at the bellhousing. I've seen pictures, and I believe it would happen, especially on conversion/afterthought addition type machines where it's not really engineered specifically to the tractor at hand, but is more of a "will fit." While the YM2000/240 series, for instance, is extremely simple, stupendously reliable, and a marvelous piece of engineered simplicity, they're fairly light in comparison to other machines of similar horsepower and size: The YM2020D, for instance, is something like 2500 lbs, while the 2000D is barely 1900.
I would feel much more comfortable with a backhoe on a 2020, as a result, than on a 2000, just as my 186D is visibly beefier than my 1401D. Knowing the tendency of people to use things to their limit and then a bit beyond, the banging around a backhoe puts onto the tractor would be better absorbed with the biggest, heaviest and sturdiest tractor possible. I wouldn't fret much putting a 6 foot category I backhoe on my 6500lb IH464 that lifts something like 3000 lbs on the hitch, while the same hoe would rip my light 1401D apart, loader subframe or not.
I'm certain that having a good subframe that ties the ends of the tractor together and gives the structural members some separation helps significantly, but integrating the mount for the backhoe into the entire structure would be much better, for fairly light tractors. It's one thing to be operated carefully by a knowledgeable operator, and another to be sturdy enough to handle rental yard duty. I think a dedicated backhoe subframe is the responsible thing with light tractors running a 3 point backhoe; I'll be the first to admit I don't own one, though I've used them.
The sheer force involved in backhoes kind of frightens me, especially when the tractors weren't originally designed for those loads. Even when they are, the 3 point style just seems like it's asking for trouble unless the backhoe is undersized for the tractor, at least in comparison with a frame mounted version.
I split a Ford 1700 a couple weeks to replace the clutch, and even though it's a markedly bigger and heavier machine than the YM240, I was (and am) uneasy about how few bolts there are connecting the back half of the tractor to the front half. If I tried to design something like that, not only would it never work, but everyone would tell me I'm an idiot.

Watching a backhoe shove a tractor up, down, left and right through the bellhousing sends shivers down my spine. I keep wanting to purchase a backhoe, but keep coming back to being nervous about the durability and longevity of my tractor(s) with it mounted. I don't have much use for one anymore, it would be more of mild convenience and a toy, but if I ever get something, I'm going to mount it semi-permanently onto a full subframe and tie into the loader frame and everywhere else possible. Realistically though I'll sell a tractor or two and substitute a skid steer equipped with a backhoe.