C++ is one of the most complex, inscrutable computer languages ever created. (...) Is that by intent, or did it just happen?
Yes and no, depending on how you look at it. Once upon a time like 40+ years ago there was C. While there was others, C was massively successful in the 1970s because it was a very good but really thin abstraction layer over assembler, which was very common at the time. That means you could write C and it'd run on many different kinds of machines, conversely if your platform wanted to go anywhere it had to have a C compiler. It was imperative and procedural, which was fine but computer scientists also wanted an object oriented language. How do you do that when you don't have a massive staff and budget? You extend C. Early C++ compiled down to C which then compiled on every platform with a C compiler. All the other very low level C-isms just came along for the ride. And any behavior that wasn't defined in C, well it couldn't be defined in C++.
A lot of it is simply the result of C++ paving the way, it was often the first C-derived language to do it and a lot of it turned into ungodly kludges, but you were pretty much committed to keeping that syntax working. So you keep adding and adding but never subtracting, never cleaning up. It's easy to say "lets start over and do a clean rewrite" but hard to achieve the necessary momentum, many have tried and failed. And with locked down devices it's now the device manufacturers that control if a given language will be available, you can make UltraC but if you can't make an iOS app in UltraC then the value is more limited. Outside Apple, Google and Microsoft I don't see who can pull it off, Sun could once but Oracle could never make a new language. Not counting web server languages like Perl/PHP/RoR, but local end user software.