I believe this is for the same reason some microcontrollers do it, to whit there is no page table and much less page access bits. These days the browser is a greater thread vector than ordinary application code.

Wasm is a Harvard architecture mostly because it wants to support implementations based on static recompilation. Obviously, self-modifying code is a problem for static recompilation, and the easiest way to prevent self-modifying code is just to not expose code in the address space at all. There's also the historical fact that wasm is a successor to asm.js, and asm.js is a Harvard architecture by virtue of the fact that JS Typed Arrays don't allow you to execute code stored in them.