"How would I trust the programmers who implement compilers that they are not goin to make any mistakes? I'll write the assembly myself, thank you very much."
It's much better to push logic from being manually re-written over and over by tens of thousands of different programmers, to being built into a language/tool/library by a team of a few hundred experts and then robustly tested.
> "How would I trust the programmers who implement compilers that they are not goin to make any mistakes? I'll write the assembly myself, thank you very much."
Nope, doesn't work. Then you have to trust that the programmer who wrote the assembler didn't make any mistakes. Real programmers program in octal.
> Then you have to trust that the programmer who wrote the assembler didn't make any mistakes.
This is true, but the actual solution is safer assembly. ARM is heading in this direction with PAC/BTI/CHERI. Intel, being Intel, tried adding some and it was so broken they removed it again.