I've been racing for years with an open (stock) diff. Not such a big deal on the faster courses and especially if you have a lower HP racer like mine. Maybe if I had 100 HP (instead of around 70, I'd feel different).
Even tighter courses like Shenandoah don't seem to really need one. There is one Mickey Mouse second-gear turn on the Pocono infield that I could use it, but it's still no big deal.
I co-drive a 1275 Sprite with a Quaife differential in some of our enduros. It has maybe 90 HP and it doesn't really seem much different than mine in terms of rear traction in turns. Even in the rain.
By the way, his Quaife seized in our last event and I helped him pull it apart. There's some cool looking "guts" inside those things.
Last year at the Glen his car snapped an axle and the car would not move afterward...just like an open diff. I though the Quaife would keep the car moving, but apparently not.
Also, the Quaife is just as quiet as a stock diff. It uses a series of worm gears to "bind" both sides together. Some other LSD diffs use a racheting "locker" that is quite noisey.
I've run a welded rear too. I did not like it. One of my friends runs a Midget in hillclimbs and likes his welded rear because if he snaps an axle (due to the standing start), he can still finish. I rarely do standing starts, so not a big deal to me.
Honestly, a lot of amateurs (like me) would be better to spend that money on tires than a limited slip diff, especially for street use.