Exactly the same thing was being said about Java (the first of the C++ killers) back in 1990s. And yet C++ is still around. It is not that easy to kill it seems.
The overall use of the language grew because everything in IT grew a lot during that time, so the niches where Java sucks grew larger than all of the C++ niches at the start.
The real question is if Rust will leave any niche. It looks like it won't, but this is not the kind of question one can really answer.
The trade-off was more overhead, but faster development and fewer errors due to not needing to manage memory or other low-level details.
Java is easier to write than C++ and is more portable than C++, but needs more time to get fast and more memory to work with.
By way of comparison, Rust offers all of the speed of C++ and similar low overhead with practically none of the footguns that C++ is known for.