My experience with stump buckets is limited to skid steers but I actually think using one on a skid steer vs a typical small tractor is probably more enlightening than the other way around.
The main problem with stump buckets is that most of them are targeted towards skid steers which have stronger breakout, stronger lift capacity, stronger loader frames, etc than most small tractors. They also weigh more which becomes a big factor when prying up with the bucket, when the ground is your fulcrum and the force you can put down on the tractor end of the bucket is limited by the weight of the front of your tractor before the wheels come up.
I think a stump bucket CAN be just fine on a tractor, IF it's sized properly and if it's used properly. Titan/palletforks.com stump bucket is one of the better designed ones for a tractor because it's lighter on its own, not
absurdly long, and has a very narrow 'tip' which means better ground penetration with limited weight/downpressure from the machine.
Even with the right one, it is all about technique. The shortest thing i can say is you are likely not going to pry ANYTHING directly out of the ground in one shot unless it is tiny. You will have to dig around cutting/breaking roots around the perimeter before going for the main stump. The approach i use to get it in the ground is point it down at a steep angle, like 60-90 degrees down, push down until the front of the tractor comes up, hit the brakes and try curling the bucket up to see if it will scratch and start to dig forward a bit. May have to let off the brakes and let the bucket curl the push the tractor backwards a bit. As the bucket gets closer to 30-45 degrees down, put the front tires back on the ground, if you got 4wd pull up on the loader just a little to load the front tires for traction, and then drive forward. As the bucket digs in and tries to go lower and lower you'll have to lower the loader arms with it to keep it from just wedging your front tires down harder and preventing it from digging any deeper. Don't try to bury the whole bucket (but good luck if you try, lol), no more than around halfway in is probably best for the initial groundbreaking. Then curl to see if you can pry it up. If you can't, push your loader down until the front wheels come up again, and continue trying to curl. That puts your max weight down on the back of the bucket, and the ground under the middle of the bucket becomes a fulcrum and you are using the bucket for 'leverage' in addition to just hydraulic curl force. If that doesn't work you can try slowly pulling backward and see if the bucket edges will 'saw' whatever you're stuck under. If none of that works you'll just have to try less depth.
A lot of small tractors have a lot more 3pt lift than they do loader lift. That being the case, you may actually think about getting a 3pt subsoiler and trying to snag and rip up most of the roots around the stump itself, before trying to get the stump itself with the loader. Plus, they're cheaper.