Ditching headers does not solve anything at least if your language targets include performance or my beloved example Gamedev =) . You will have to consume headers until operating systems will not stop using them. It is a people problem not language problem.
Big elephants in the room I do not see in your list:
1) "threading" was bolted onto languages like C and C++ without much groundwork. Rust kinda has an idea there but its really alien to everything I saw in my entire 20+ career with C++. I am not going to try to explain it here to not get downvoted into oblivion. Just want you to think that threading has to be natural in any language targeting multicore hardware.
2) "optimization" is not optional. Languages also will have to deal with strict aliasing and UB catastrophes. Compilers became real AGI of the industry. There are no smart developers outsmarting optimizing compilers anymore. You either with the big compilers on optimization or your language performance is not relevant. Providing even some ways to control optimization is something sorely missed every time everything goes boom with a minor compiler update.
3) "hardware". If you need performance you need to go back to hardware not hide from it further behind abstract machines. C and C++ lack real control of anything hardware did since 1985. Performant code really needs to be able to have memory pages and cache lines and physical layout controls of machine code. Counter arguments that these hardware things are per platform and therefore outside of language are not really helping. Because they need to be per platform and available in the language.
4) "libc" is a problem. Most of it being used in newly written code has to be escalated straight to bug reporting tool. I used to think that C++ stl was going to age better but not anymore. Assumptions baked into old APIs are just not there anymore.
I guess it does not sound helpful or positive for any new language to deal with those things. I am pretty sure we can kick all those cans down the road if our goal is to keep writing software compatible with PDP that somehow limps in web browser (sorry bad attempt at joking).