Wow. That was hard to watch.
I wouldn't put that snake down if it was able to feed and basically function, but I would question the ethics of breeding the spider gene knowing that the wobble is part and parcel of it. I know other morphs have their issues, like how super lessers sometimes have bug eyes. But it doesn't seem like the bug eyes really affect the snake's quality of life; it just looks goofy (correct me if I'm wrong, though). That might also be a reason to avoid producing the super form, but not a reason to avoid breeding lessers at all if only one copy of the gene doesn't produce that defect.
It would be very hard to make the case that a severe wobble like in the video doesn't affect the snake's quality of life. Who knows how much the snake really is or isn't suffering when that happens; maybe it's frustrating, maybe it's terrifying, maybe it's neither. But I doubt it's pleasant. OK, some spiders barely wobble at all and there are lots of spectacular morphs that have that gene, but knowingly propagating a genetic issue like that is not something I would do.
All that said, I'd be really interested to know how your "exercise program" works out! I think it's completely plausible for exercise to help mitigate that condition, whether by improving balance/equilibrium, improving muscular control/coordination, developing and reinforcing a wider variety of pathways for motor control, or just increased strength providing better stability. Like occupational therapy for snakes!