You are right, some of the issues highlighted in the paper could be solved by compilers targeting WebAssembly. One such mitigation that is (currently) missing are stack canaries. In contrast, stack canaries are typically employed by compilers when targeting native architectures. They also cost performance there (typically single digit percentages), but evidently compiler authors have decided that this cost is worth the added security benefit, since fixing "old C issues" in all legacy code in existence is not realistic.
Note however, that other security issues highlighted in the paper _are_ characteristics of the language, notably linear memory without page protection flags. One consequence of this design is that there is no way of having "truly constant" memory -- everything is always writable. I do think that this is surprising and certainly weaker than virtual memory in native programs, where you _cannot_ overwrite the value of string literals at runtime.