It is seldom a good idea, or even sane, to choose to machine something out of titanium (or beryllium). But sometimes there are reasons.

I think C++ does a decent job of being as logically expressive as practical while still supporting C-level memory micromanagement. Typically exposing C-level memory micromanagement issues is a bug, but occasionally it's a feature. So to me, the point of C++ is to express abstractions like polymorphism and exceptions in the same few pages of code as low level memory operations. How often do I want to do that? Not very often, but it can happen.

Also, while C++ is very hairy and I wouldn't want to have to implement it, C++ seems to be implementable enough and standard enough that it may be usefully supported on a platform well before other more expressive languages. Perhaps it's because a lot of the C++ hair is frontend target-independent stuff like parsing and templates, so that once you've ported the C backend you're almost done porting C++ too? Dunno for sure why, but it seems to happen: e.g., it was my impression on my Atari ST many many years ago, and is my casual impression that something similar happened for the Arduino more recently.

C++ is admittedly a weird mess in various ways, but given the choice of source almost-compatibility with C (which I don't particularly value, but which I can at least understand) and C-level linkers (which I have mixed feelings about) a mess seems inevitable. Thus, I still consider it an impressive design.

Occsionally I've seen IMO-excessively broad claims that higher level languages are the best. It sometimes makes me think I might be able to cook up an example where C++ would be hard to beat: a small backtracking search problem where trailing operations (in the sense of "trailing" that you'll see if you Google "trailing backtracking") are in the inner loop. Take this thought of mine with a generous amount of salt, because I've never boiled it down to a really clean challenge. OTOH, I have at least implemented such search in several languages, and I even did a few casual benchmarks --- but 10+ years ago, when performance tradeoffs were rather different.

That's a particular case of a general theme where C-level programming could win: performance dominated by a very simple memory allocation regularity (LIFO, in this case) that the GC doesn't know about. (This theme also involves the precondition that you should care more about a factor of 2 in performance than a factor of 2 in programmer time, which often doesn't hold.) In many instances of this theme, the accreted featuritis bloat of C++ would be overkill, so you'd prefer C. In this instance, though, placement new() of polymorphic objects into LIFO-allocated raw memory is more expressive than anything I can see how to do in C.

Now, we should not forget that many programmers can go all year without running into a single problem where a factor of 2 in performance is worth a factor of 2 in programmer time. And we should not forget that even the ones who need to care deeply about performance often find it's not determined by a few low-level hotspots where low-level tweaking helps. But in some subfields, it's not too unusual to rationally choose to micromanage stuff at the level of C/C++. (I nominate the subfields of embedded programming and compute-heavy search from personal experience, and Quake/Unreal-like engine programming by reputation; I also explicitly do not nominate implementing web browsers, ow ow ow.)

It's harder to think of reasons I'd choose to write sizable programs in C++ (other than the compelling but unsatisfying accidental-seeming reason of early availability on a platform). One reason, though, is that there are many subproblems for which the choice of language doesn't matter all that much. E.g., Fortran is adequately expressive for a lot of the stuff in a book like _Numerical Recipes_, and you can famously write Fortran in (almost) any language. Because of this, I sometimes encounter a program where some key subproblem really cries for a particular style of language, possibly C++, and then I can be language-agnostic about solving the other subproblems, not minding writing it in whatever language I chose for the key part.