That tractor looks exceptionally clean and well taken care of THAT'S what I would be shopping for.
It looks like the BT600 backhoe mounts to a partial backhoe frame that's good, I found the BT600 user manual
http://geckocycles.com/images/sagauro/BT600 owners.pdf and from what I see Kubota mounted a partial backhoe frame on the rear of the tractor for the backhoe to attach to. PTO mounted backhoe is a bad idea imo.
My BH65 hoe on my
B2920 mounted to a full frame. Basically two large thick steel plates that ran from the rear where the backhoe attached all the way forward along the tractor frame out forward of the dash just back from the front tires. The hoe can lift the entire tractor off the ground and typically I had the tractor resting on the backhoe stabilizers and FEL bucket, the rest of the tractor lifted in mid air. Even with all that weight the hoe can and did lift the tractor off the hoe stabilizers, hence mounting it to a thick steel frame is a good idea.
I found my backhoe useful beyond just digging. With a mechanical thumb (I found some pictures of a BT600 with a bxpanded bolt on thumb) I frequently would grab with the hoe bucket/thumb logs and large branches, grip them in the middle and hack away with my chain saw. Also useful for grabbing onto a stump and lifting up out of the hole. One was so large even the hoe couldn't lift it, but I was able to grab it and drag it out of the hole driving the tractor forward.
That said, my need for a backhoe did come to an end. After the trees and bushes were cleared, stumps dug, drainage lines in, the backhoe sat in the garage unused other than ballast for the FEL. Hence I did not purchase a backhoe for my
BX2380. If one day I need a hoe for some job I'll just rent one for a lot less than the $7k they want for a new hoe for my BX.
Backhoes are good tree root breakers. Even my BH65 had limits, it could not just grab a 6 inch diameter Fir tree root and break it, the hydraulics would max out before the root budged. No problem, instead I used the backhoe bucket teeth to rip my way through the root a couple inches at a time, munching on it. Another tactic was moving out away from the stump 6 to 10 feet where the root was thinner, ripping it up out of the ground from there, digging the dirt out from either side of the root. Dirt is the stumps strength, remove the dirt and its MUCH weaker.
These are not huge industrial excavator hoes so learn the limits and devise strategies to get the job done in smaller bites. Neighbor across the street from me clear cut 3 acres of fir trees. Pretty good size trees up to 3 foot in diameter. It took a full on bulldozer with a stump splitter and industrial excavator to remove those stumps in two pieces. Fir trees have tap roots that bore straight down into the ground several feet even the big industrial excavator could not just grab those and rip them out of the ground.
My point here is if guys start recommending moving up to a B tractor to get the next size larger hoe, that never ends. You can keep on making an argument to keep on moving up in size to bigger and bigger hoes but they all have their limits even the large industrial excavators so meh, the BX hoe will be fine within its limits. May take you a bit longer to finish a job, and there may be some jobs it just can't handle but that's true of any size hoe. 3 of the many trees I had cut down were fir trees about 2 foot in diameter. I dug a huge hole around those stumps, munched my way through all the roots, only thing left was the tap root, my BH65 could not even budge those stumps. I ended up hiring a stump grinder to come out and grind them below grade. But it managed to dig out all the other stumps, a few dozen of them.
One last thing my hoe was good for, digging fence post holes. My neighbor rented one of those 2 man augers, FAIL! The clay and tree roots some of them several inches in diameter, I think he worked for an hour and still had not finished digging 1 post hole. The backhoe was able to dig the holes and rip through all the roots. He then used the round cardboard tubes they use for cement footings, put those in the holes, packed the dirt in around them, put his fence posts in those and shoveled in cement, worked perfectly. I dug all his fence post holes with the backhoe in about 2 hours.