Why is this design requiring a torsion spring so popular? Space savings due to the sectioned door?
The house I lived in as a kid had a solid metal door hinged about 3/4 of the way up, that you could lift by hand with relatively low effort, and at the top position it would balance on its own weight. The electric part was just a roller chain attached to a short lever, which also happened to give some resistance to the closing movement.
I think it's because of the space saving. We park our cars in front of the garage, and wouldn't have enough space on our driveway to allow for the door to swing out and not hit a car parked there. Also most garage doors aren't see-through, so you may not know if a car is parked there at all, leading to a high number of fender dings.
Not unless you consider licensed garage door technicians to have superhuman abilities beyond the reach of mere mortals. I would expect anyone who puts this much care and calculation into the job to be more than capable of completing it successfully.
On the other hand, many things require time-consuming training and/or experience to do correctly and safely. So no-one can be expert in everything. Often it's simply better to pay someone who has the relevant expertise to do a specialised job.
I replaced one. Simple idea: The spring is only dangerous when wound, so why not just have it just mildly tensioned and hook the lift wires up to the garage door when it's in the "up" position?
It worked too, after about 50 tries per side! With the confined space, and only two hands, getting those wires to stay in the spiral groove of the pulley while also hooking them up to the door is... error prone. Can't even ask for help because the raised garage door blocks access.
However I got it done in the end, and the spring was never tighter than you can wind it with one bare hand. The garage door works fine.
I did watch someone do it the proper way (wind it to full tension with the door down) and agree, you could hurt yourself that way.
This isn't particularly hazardous for a typical residential door. However, I would NOT recommend average Joe doing this on anything over an 8x12 door, or a door with glass windows. I've seen people thrown and bars explosively hurled on heavy doors (with heavy springs) during unexpected failures/incidents.