Call my insurance when I have a broken engine? Sounds odd to me, what am I missing here?

No, I'm not planning to do that, but it's advice I've seen before and just had someone else mention to me that I should call my insurance re the blown engine on the BRZ, assuming that they cover "driver improvement" (which I'm about 99.5% sure they don't).

As a European, this sounds a tad odd to me as I'm used to regular car insurance not covering mechanical mayhem unless it was caused by an accident (and that's assuming I have full coverage). Does US car insurance actually cover engine failures if you have full coverage on a car, or am I missing something here?

They don't unless it's part of an accident.  I'm not in the insurance business.  

Nothing I've ever heard. That sounds more like wishful thinking from a kid who just nuked his engine hammering on it like a fool.

As I understand it, mechanical defects are handled by the manufacturer and whatever agreement they have with the car's owner.

OK, looks like I wasn't too far off then. I always assumed that vehicles that were "mechanically totaled" and show up at Copart et al would've been sent their by a warranty provider and not regular insurance.

I have had extended maintenance/repair added on to insurance before. It is an add-on and not part of the regular insurance.

I've seen/heard of it once: Large object comes off of truck in front of the car on the highway, large object cannot be avoided, large object hits just right and punches gigantic hole in the oil pan. New engine, insurance paid for it.

Otherwise, it can't hurt to call, but I'd be shocked if it was ever covered - but I've only ever read my own auto policies that have been from only 2 companies. Maybe yours does it differently.

I have never heard of insurance covering basic mechanical failure either, but it's worth noting that insurance regulation varies a lot by state and it's conceivable that there's one out there where it does.

I expect engine damage resulting from a collision would be covered as would that from a fire (with comprehensive).  It would probably also be covered if the engine failed while the car was being stolen, at least if you could make a case that the thief had damaged the engine by driving it badly.

Knock the oil pan off with a rock, covered.  Forget to top up the oil, no.  Drive through a puddle and hydrolock it, covered.  Blow a head gasket and hydrolock it, no.

Streetwiseguy said:

Knock the oil pan off with a rock, covered.  Forget to top up the oil, no.  Drive through a puddle and hydrolock it, covered.  Blow a head gasket and hydrolock it, no.

This.

DW went through a deeper-than-it-looked puddle in her 2.4 swapped Neon while in mama bear mode trying to get to the kids during a terrible storm.  Insurance covered it.

I work in the industry, the comments here are accurate.   All policies have a definition of what an "accident" is and have exclusions for mechanical failure.  

Back when I had geico there was definitely an option for something like "mechanical repair coverage". I never used it but assumed it was something like "take car to shop, pay for repairs, get all but the deductible refunded". I would assume there was some system where if it was very clearly caused by operator error and not just random mechanical failure it wouldn't be covered.

People driving through deep water and hydrolocking the engine can claim and I've seen it multiple times. My favorite was the lady that hit a road gator on the highway in her 2006 Acura RL with 17k miles. Ripped the condensor and radiator in half, severed teh trans cooler lines. She continued driving for another 45 miles before the car locked up. The trans was smoked. The engine physically siezed. Insurance had to buy new parts as it was in their policy that under a certain age and mileage OE parts must be used. I loved that silly lady. She made my bonus NICE that month.

Mechanical failure by itself = not covered.

If a wheel falls off, the subsequent damage would be covered but the lug nuts/studs would not be.

Owner stupidity (such as hydrolock from driving into deep water) would be covered.

A broken BRZ engine is pretty common, BTW. They have issues.