if you have enough acres and wanting future plans to redo your land. then backhoe can pay for itself. but if you are on small amount of acerage. and not really needing to do a whole bunch. then it may be easier just renting a mini ex. when needed (save up projects and do them all at once) vs having a 3pt hitch with subframe backhoe for tractor.
stump removal, putting in gas, electrical, water, telephone, internet lines, (to house or to shed). putting in a new septic field, digging a hole for pond or swimming pool, moving heavier items in and out of truck bed or off of trailer. vs using FEL on tractor. some use backhoe with a thumb to hold up trees, to be cut, vs bending down to cut them. go with a hyd post hole digger or hyd post hammer on backhoe. to make it easier to position auger/posts. getting yourself unstuck (backhoe needs to be on) when ya drive to far into a muddy mess. have used it a few times, to make holes for plants / new trees. and also move flowers from one flower bed to other, but just taking a bucket worth of dirt and taking flowers at same time. if you need to drive back and forth on property 1/4 mile or more. i will load the backhoe bucket up with dirt and FEL up with dirt. to make less trips across the property (assuming you have a larger bucket on backhoe to make it worth while) backhoe = good counter weight for using FEL. the outriggers of backhoe, make nice "jacks" to put chains on rear tire or take chains off by lifting rear tires off ground some.
backhoes are not great for, cleaning out a lake, that has been there for a couple years or longer. due to backhoes only have 180 degree swing side to side, vs an excavator that can do a 360 degree turn to dump spoils. also excavator more easily move pads around to get in and out of a lake side.
a tracked excavator. more likely easier to dig in a small area and possibly cross a small width trench. vs a TLB (tractor loader backhoe)
if your tractor is setup for a backhoe, so you can do a 180 in seat on operate backhoe your golden. but if you have to hop off of tractor seat and then walk around tractor to get on backhoe seat. you are in for a good amount of miles walking back and forth between seats along with frustration.
backhoes when on tractor make a tractor "top heavy" and i have been known to adjust backhoe so it swings up towards the hill. so i can adjust COG (center of gravity) and reduce risk of rolling over as i go across some hills.
needing a taller garage door, and/or area within the garage. so you can attach/detach backhoe within garage. without bring the shed down onto you. *looks innocent* i tried to take house down errr the eve of the roof... *working to close to house and not paying attention that split second*
working in woods, or driving under trees. and limbs catching the backhoe, when it is in transport position. a couple trees here have had some "growing pains" as you look up into them and see a few limbs torn/twisted up.
more chance you may want to drive backwards up a hill vs driving up a hill in forward. so you do not flip backwards. due to heavy weight of backhoe on rear of tractor.
costs of buckets, and having a smaller width "trench bucket" and then a larger width bucket, for digging out holes.
costs of hyd thumb. extra hoses, valve, or mechanical thumb. a thumb turns a backhoe with bucket into like a grappel for FEL (front end loader with bucket)