You don't need big tires to put a big strain on the axles and gears. When you turn, the inside wheel wants to run around something like a 14' radius, and the outside wheel around a 19' radius (depends on size of vehicle, but 60" track is average). This makes the two axles "fight" each other -- the outer wants to go faster, the inner slower. So the axles try to twist and the tires grind each other down. Whichever is weakest loses, but all parts get a lot of strain. Nothing will break right away, but the added strain will cause a lot quicker failure -- something WILL eventually break, and when it does, it will be catastrophic.
Ever seen or heard a car snap an axle? I've been close by when it happened at a dirt track -- welded differential broke in the pit area when the guy was turning the car around. We thought someone had fired a shot gun! Needless to say, no racing for that guy that night. A spool (or even mini spool) would hold up a bit better than welded spider gears due to the heat caused by the welding. That just means the spool/mini would cause a bigger bang when it broke.
The solution is a locker for street/strip use. If you don't like the ratcheting noise of a limited slip, get something like an air locker made mainly for 4x4 vehicles. Those lock on demand, and are really safer than a limited slip. Even limited slip is dangerous on slippery surfaces (wet, icy, loose sand, etc.). Once the wheels lock it's just like a spool -- the car will slide sideways with both wheels spinning and the driver has less control over the vehicle. The air locker only locks when you ask for it.
A local rodder with a blown 350 in a 'glass 32 decided to see if he could break the wheels loose at 50 mph in high gear, so he floored it. Sure will break them loose! Slid sideways and went off the road, causeing a little frame damage. Luckily just the running board and fender on one side were destroyed, and a slightly bent frame -- no people damage (except for some clothes...). With a "one legger" only one wheel would break loose and the other would maintain enough traction to keep the car from sliding sideways.