If your car seatbelt was cut, would you just stitch it back together with your grandma's sewing kit and call it a day? No.
I've made some webbing straps using grandma's sewing machine with ordinary polyester thread and they're totally OK for the intended use (hitching a heavy load to a winch and winding it up a steep ramp). There's really nothing special about it, get the tension right and put enough stitches in to spread the stress. I keep meaning to restitch them with some heavier bonded thread, but they show no sign of failing (and if they did it would mainly just be inconvenient). The proper thread to use for seat belts is UV-protected bonded polyester, which stretches less than the equivalent nylon and I'd buy some of that if I was making up a safety harness. Old hand crank machines arguably do a better job than industrial machines as the low speed means the thread doesn't get heat stressed.