If a fuse is blown, can it cause any kind of fault light to....light up? Does that even work like that?

 

What? No, of course not. It would be a really handy feature, and I've thought of it before, but it would add a fair amount of cost to the car which 99.9% of customers wouldn't notice or care about, so because of that it doesn't get done.

If our cars were designed like military jets or something like that where easy serviceability in the field is extremely important, they'd probably have a feature like this. But on consumer products, the only features you'll find are usually ones which regular Joes (who don't work on their own cars) demand, like CD players, power windows, etc.