You can of course just ignore those when writing kernel code- they get ignored in application code much of the time! But I suppose at that point it could be argued that you're just writing C with a C++ compiler?
You can lose new/delete and .bss statics and still write reasonable, even "safe", C++. Rust doesn't have .bss statics by design (lazy_static emulates this for you though). new isn't necessary for the "modern" C++ safety stuff and you can write pretty good modern C++ without new. All new gets you is a nice wrapper around allocation, and when writing a kernel you can't and shouldn't allocate anyway. In Rust, too, you would not be allocating, either via memmap/malloc or via Box::new().
So it wouldn't be "C with a C++ compiler", it would be "C++ without allocations", which is a restriction from the problem statement anyway.
Further, even in C I rarely see use of "#pragma interrupt"-like tools- rather, everyone still seems just to use per-platform assembly glue code. (To be fair, my experience is mostly in kernel code for things like Linux, rather than standalone embedded applications where "#pragma interrupt" would be more valuable.)
Ultimately the Rust OSes resort to some handwritten assembly as well. I think that's going to be a constant of writing a kernel. Rust is working to minimize it (e.g. with things like `extern "x86-interrupt" fn`), but at a kernel level there are just some kernel specific asm instructions (like all of the TLB stuff) that either compiler will probably never support generating without inline asm.
So while Rust may be better than C++ at writing OSes (I'm not sure! I haven't looked at all the stuff you need to write an OS in C++), I do think they're in the same ballpark, close enough that if Rust is a "serious" competitor C++ probably is too :)
I thought C++ had naked functions and all the things you need to write an OS.