But there are some things to check and consider. For example if you have a Subaru or any other vehicle with permanent all wheel drive (no center viscous coupling) then there's a good chance that destroying a single tyre will result in you needing to replace all four. Because of the design of those all wheel drive systems they just don't tolerate tyres with radically different tread depths (and thus radii). Road hazard insurance only covers the one tyre that had the damage.
Also worth considering that tyre failure because of manufacturing defects, while rare, would NOT be covered by this sort of plan. Instead it would be covered by the manufacturer warranty.
You might ask how a $20 stake can give you a full replacement tyre. Surely the tyre stores would go out of business? Not really. It's a straight numbers game. The number of people who take this insurance far, far, far outweighs the number of tyres that they'll ever need to replace due to catastrophic failure. Tyres these days are pretty damn well made.
So should you take the insurance if offered? Honestly I would. $80 for no quibble coverage on four tyres is also a numbers game. If even one of your $200 tyres suffers this sort of damage, you still only paid $80 to have it replaced.