Your compiler vendor has to pick a (reasonable) behaviour though and apply it consistently, and while they are not required to document it (IIRC - I think that's just for implementation-defined?) you can probably get them to tell you if you have a good support relationship with them. Or you can just figure out what the compiler does, and hope they don't change the behaviour too much with the next release :-)
I suspect you do not want your car's brake controller to do this.
These are just some obvious cases. Not to mention that any use of operator new is UB if memory allocation fails and the system can't throw exceptions.
That's probably not great and might leave data in a bad shape, but it seems better than "undefined behavior" aka no guarantees whatsoever, no?
What compiler does it? At least g++ does not. It is not what specification dictates either.
I can't see how it is a superset either. If the library returns an Option, the calling code can process it as it please, including throwing an exception. On the other hand, if the library only indicates error by throwing an exception, it cannot work with the caller that is built with exceptions disabled.
Otherwise, I should point out I explicitly said "at() with exception support enabled". It's also important the ability to disable exceptions is not a feature of C++, the C++ specs assume exceptions work (just like the Java or C# or Go specs). It is a feature of certain C++ implementations that they suport this mode, just like they support other non-standard features (compiler intrinsics, various #pragmas, etc).
Disabling exceptions is indeed not in the standard, probably because of Stroustrup's position (I respect many of his opinions, but cannot agree with this one) - but it's what every sane compiler, especially a one targeted at embedded systems, will support. Exceptions are designed for a controlled environment where a program terminating will return to somewhere that will maybe add a line to a logging system and restart it automatically. It only complicates things when terminating is an unacceptable scenario.
Regarding exceptions being more code, I very much don't agree. Even for embedded apps, the pattern of "if this fails, wind back up to some top level event loop" is quite common, and exceptions give it to you for free if you're also using RAII. In contrast, with Result<T, E> you have to write code at every level of the stack to handle it. Code which gets particularly ugly when you combine it with things like map() or filter().
The main reason people use C++ over safer languages like Java is performance (memory, CPU speed, real-time constarints etc). And C++ the language is designed for performance, but only with an expectation of a very powerful optimizing compiler. Most C++ std classes are extraordinarily slow and inefficient if compiled without optimizations - certainly much slower than Java for example.
So, C++ is not really C++ without aggressive optimizing compilers. And one of the biggest tools that compiler writers have found to squeeze performance out of C++ code is relying on UB not to happen. That essentially gives the optimizer some ability to reason locally about global behavior: "if that value were nullptr, this would be UB, so that value can't be nullptr so this check is not necessary". And this often extends to the well defined semantics of standard library classes outside their actual implementation - which rely on exceptions.
So, to get defined behavior out of the std classes in the absence of exceptions, either you disable many optimizations entirely, or you carefully write the optimizer to have different logic based on the no-exceptions flag. But, all C++ comittee members and C++ compiler writers believe exceptions are The Right Way, for every situation. So getting them to do quite a lot of work to support someone doing the wrong thing would be very hard.