Yes, wire-wrapping is/was so great. Really good quality connections, no accidental connections due to solder ending up at the wrong places, easy to remove or change.
And no solder-iron that risks burning stuff. And no smoke either.
The only draw-back is that it seems to be so expensive and almost non-existant today.
Burning stuff isn't a problem when soldering. It sounds like you need a little equipment upgrade. Get a holder for your soldering iron, and a fume extractor (filtered fan).
I wasn't mainly thinking about the actual soldering process, although that can also be an issue with small components or when not focusing on where the iron touches while reading a schwematic. But more like when the solder iron is stuffed back in the holder and something else gets pushed against it or when I get stuck in the solder iron's power cable and the solder iron is pulled out of its holder. I guess with more space, less junk on the table and the power cable fixed somewhere would help, but still, it's an annoyance.
I would prefer holding a wire-wrapping pistol than an iron.
And no solder-iron that risks burning stuff. And no smoke either.
The only draw-back is that it seems to be so expensive and almost non-existant today.