I find this statement hard to imagine. I've been coding professionally in C++ for just shy of 20 years now (and in C for a few years before that) and have only resorted to assembly when I needed to actually use assembly for performance reasons.
Actually - not completely true. I do like to look at the assembly from time to time for other reasons, but this is rare.
Even when I have performance to worry about, intrinsics are usually an option - possibly even a superior option - when writing performance sensitive code. But here are some of the cases where I resort to looking at program disassembly - I'll note a theme here of debugging optimized code (because who doesn't love heisenbugs):
1) Diagnosing a crash which turned out to be the result of a 1 byte vtable pointer corruption bug in an older codebase, which turned out to be a bad static_cast in relatively removed code (a good case for boost::polymorphic_downcast!). Simply understanding which pointer was bad in the first place required looking at the disassembly - when you can't rely on your debugger's results thanks to optimization.
2) Figuring out the actual values of variables in crashes and crash dumps of optimized builds to properly root cause a bug, when the debugger gets confused - or simply aggressively inlined and reordered everything so aggressively that there's no sensible values to even display (so, most crash dumps.)
3) Noticing when the optimizer has reordered code "unexpectedly", alerting me to the fact that supposedly thread safe code is in fact nowhere nearly remotely safe and is in fact missing many memory barriers (possibly because their portable macros "helpfully" defaulted to a noop on whatever new and previously unrecognized platform I'm porting to.)
4) Noticing when the optimizer has removed or rewritten code in an "incorrect" manner, helping me debug code that would've worked if it hadn't technically invoked undefined behavior, so I can a) fix it, b) attempt to explain to my coworker that, yes, it's really undefined behavior, and yes, it's actually a problem (typically with a combination of citing the standard and linking INVALID WONTFIX-ed "bugs" in some compiler's bug database), c) be reasonably certain I've actually found the real root cause of a bug and fixed it.
Now, yes, I'll admit this isn't 100% of my debugging sessions. And perhaps I'm an outlier. My coworkers generally learn that I can (eventually) tackle pretty much any weird bug they might be struggling with and that I'm happy to help. All the porting I've done reopens a whole codebase's worth of wounds - latent undefined behavior that another compiler's optimizer didn't take advantage of.
But on the other hand, I've been lucky enough to never encounter a codegen bug in all the compiler and linker bugs I've found. So far. That I know of. And while "rare" by incidence, these are the debugging sessions that can eat weeks at a time for a single bug, when sufficiently nasty and novel.
Actually - not completely true. I do like to look at the assembly from time to time for other reasons, but this is rare.