The photos are of what I believe is a Dearborn 4 point mount for a backhoe on a hundred series tractor. I am of the opinion that a full sub frame is a necessary component to have along with the backhoe due to the stresses involved from the weight and forces applied.
If the Bush Hog loader is the quick disconnect type, then you don't have a full loader frame that connects to the rear axle, just a mid mount on a main casting of the tractor. Now you add this 3 point backhoe without the sub frame, you have weight and forces imposed in 2 places, on just the tractor itself. Use the hoe in an abusive manner and there is no doubt about doing damage to the tractor at some point.
Consider how a 555 backhoe is built and study the frame, it will help understand how they reinforced the tractor for an industrial application such as a dedicated tractor loader/backhoe.
A 3 point backhoe can be had in many sizes and most are a lot less weight than any backhoe such as a 555 for example. Also realize you won't or should not be doing the heavier work a dedicated TLB is designed for, so it is a much lighter application well suited for a lot of common tasks that otherwise could be labor intense by hand. Still a useful tool, but with limitations.
I've run these on small compact tractors, Kubota and Kioti, both with subframes. They are decent, but nothing like a full size backhoe.
Honestly, I think they are fine if properly installed, reinforced and not operated in an abusive manner. Shock loads will cause damage and one thing I can think of is the pin boss on the rear axle housing for the top link. My 850 ford has a 4 point mount on it, connected to a Wagner loader frame and the pin boss on the rear axle housing has a fracture line in it and the loader frame was broke right by the foot rest. Now, this one had a Sherman power digger on it at one time, they have some bulk and weight to them, likely more than most 3 pt models out there today, and more than in the photos below. That is a good thing, smaller and lighter, with a subframe just makes sense for one of these.
I've considered one as well, but just decided it was far better to go for a conventional TLB, which ended up being a pretty decent low hour 555-C, for a few reasons. It's meant for the purpose and is ready to use anytime vs changing attachments out on my 4630. It's nice to have a dedicated tractor for this, ready to use.